Exponential decay function

How to Solve Equations With Exponential Decay Functions

Exponential decay - Wikipedi

An exponential function a⋅rˣ is growing (increasing) if r>1 and decaying (decreasing) if 0. An exponential function a⋅rˣ is growing (increasing) if r>1 and decaying (decreasing) if 0. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org. Start studying Exponential Decay Functions. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Search. Browse. Create. Log in Sign up. Log in Sign up. Exponential Decay Functions. STUDY. Flashcards. Learn. Write. Spell. Test. PLAY. Match. Gravity. Created by. bianca_ortiz48. Terms in this set (18) Chelsea is graphing the function f(x) = 20()x. She begins by. While function with exponential decay DO decay really fast, not all functions that decay really fast have exponential decay. For example, consider \(f(x) = \frac{1}{x^2}\). If you graph this function, you will see it decays really fast, but it actually does not have exponential decay. If you were to describe exponential decay, beyond the algebraic terms of its definition, you will need to say. exponential decay functions. STUDY. Flashcards. Learn. Write. Spell. Test. PLAY. Match. Gravity. Created by. alavaz_ailicec. Key Concepts: Terms in this set (14) the table represents an exponential function. x= 1,2,3,4 y= 6,4,8/3,16/9. B. 2/3. two exponential functions are shown in the table. x , f (x)=2^x , g (x)=(1/2)^x. B. the functions f (x) and g (x) are reflections over the y-axis. the. Table comparing Exponential growth and Decay . Summary of Exponential growth Vs. Decay. Both exponential growth and decay can be described mathematically using equations involving an exponent. Both exponential growth and decay involve a rapid change in numbers. The exponent for exponential growth is always positive and greater than 1

Exponential Decay: Definition and Function

  1. Probably the most well known example of exponential decay in the real world involves the half-life of radioactive substances. Example. of Equation & Graph of Exponential Decay Function. Property #1) rate of decay starts great and decreases ( Read on, to learn more about this property, which is the primary focus of this web page
  2. Exponential Growth and Decay Exponential growth can be amazing! The idea: something always grows in relation to its current value, such as always doubling. Example: If a population of rabbits doubles every month, we would have 2, then 4, then 8, 16, 32, 64, 128, 256, etc! Amazing Tree . Let us say we have this special tree. It grows exponentially, following this formula: Height (in mm) = e x.
  3. As such, exponential functions are used to model a wide range of real-life situations (such as populations, bacteria, radioactive substances, temperatures, bank accounts, credit payments, compound interest, electricity, medicine, tournaments, etc.). Any quantity that grows (or decays) by a fixed percent at regular intervals is said to possess exponential growth or exponential decay. In.

The figure above is an example of exponential decay. In fact, it is the graph of the exponential function y = 0.5 x. The general form of an exponential function is y = ab x.Therefore, when y = 0.5 x, a = 1 and b = 0.5. The following table shows some points that you could have used to graph this exponential decay How to write exponential growth and decay (half-life) functions. This video is provided by the Learning Assistance Center of Howard Community College. For more math videos and exercises, go to. Exponential decay also happens, for example radioactive decay and the absorption of light. One example of an exponential function in real life would be interest in a bank. If a person deposits £100 into an account which gets 3% interest a month then the balance each month would be (assuming the money is untouched)

A function of multiple overlapping Sine curves, consisting of diverse wavelengths and amplitudes with an exponential decay, is constructed. kst-chemie.ch E s entst eht ei n Funktion v iel er überl ag erter Sinunswellen verschiedener Wellenlängen und Amplit ud en m it e in em exponentiellen Zerfall Things to Remember About Exponential Function (EXP) in Excel. The Exponential function in Excel is often used with the Log function, for example, in case, if we want to find the rate of growth or decay, in that case, we will use the EXP and the LOG function together. We can also use the POWER function in place of the Exponential function in. Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x is the exponential function and N_0=N(0) is the initial value. Exponential decay is common in physical processes such as radioactive decay, cooling in a draft (i.e., by forced convection), and so on

So let's just write an example exponential function here. So let's say we have y is equal to 3 to the x power. Notice, this isn't x to the third power, this is 3 to the x power. Our independent variable x is the actual exponent. So let's make a table here to see how quickly this thing grows, and maybe we'll graph it as well. So let's take some x values here. Let's start with x is equal to. In probability theory, an exponentially modified Gaussian (EMG) distribution (exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean μ and variance σ 2, and Y is exponential of rate λ.It has a characteristic positive skew from the. [Solved] Fitting exponential decay function. Follow 430 views (last 30 days) Grant Huckels on 25 Jul 2019. Vote. 0 ⋮ Vote. 0. Edited: Image Analyst on 3 Feb 2020 I'm trying to fit an exponential decay to a dataset of x and y values (3001 each). Using other software I was able to calculate a k_off around 0.02 however using the fittype and fit to replicate this in MATLAB I get the following. Exponential Decay: y = a(1 - r) x. Remember that the original exponential formula was y = ab x. You will notice that in these new growth and decay functions, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r). The growth rate (r) is determined as b = 1 + r. The decay rate (r) is determined as b = 1 - r . a = initial value (the amount before measuring growth or. Exponential growth and decay often involve very large or very small numbers. To describe these numbers, we often use orders of magnitude. The order of magnitude is the power of ten when the number is expressed in scientific notation with one digit to the left of the decimal. For example, the distance to the nearest star, Proxima Centauri, measured in kilometers, is 40,113,497,200,000 kilometers

Exponential Growth and Decay Exponential functions are of the form Notice: The variable x is an exponent. As such, the graphs of these functions are not straight lines. In a straight line, the rate of change is the same across the graph. In these graphs, the rate of change increases or decreases across the graphs exponential decay function y = exp*(-Tau.time) Follow 210 views (last 30 days) Nabin SUNAM on 30 Jan 2015. Vote. 0 ⋮ Vote. 0. Answered: Mischa Kim on 30 Jan 2015 Accepted Answer: Mischa Kim. Another exponential decay function I am having problem with: Need to write script to plot the following equation. y = exp ^ -(timeconstant*time) prompt the user for beginning and ending values of time. In an exponential decay function, the base of the exponent is a value between 0 and 1. Thus, for some number b > 1, b > 1, the exponential decay function can be written as f (x) = a ⋅ (1 b) x. f (x) = a ⋅ (1 b) x (mathematics) Having two summed exponential terms.··Such a function or expressio Exponential functions follow all the rules of functions. However, because they also make up their own unique family, they have their own subset of rules. The following list outlines some basic rules that apply to exponential functions: The parent exponential function f(x) = bx always has a horizontal asymptote at y = 0, except when [

dict.cc | Übersetzungen für 'exponential decay' im Englisch-Deutsch-Wörterbuch, mit echten Sprachaufnahmen, Illustrationen, Beugungsformen,. The exponential function is one of the most important functions in mathematics (though it would have to admit that the linear function ranks even higher in importance). To form an exponential function, we let the independent variable be the exponent I am trying to fit exponential decay functions on data which has only few time points. I would like to use the exponential decay equation y = y0*e^(-r*time) in order to compare r (or eventually half-life) between datasets and factors. I have understood that using a linear fit instead of nls is a better alternative for this particular function [1,2], if I want to estimate the confidence. I would use the scipy.optimize.curve_fit function. The doc string for it even has an example of fitting an exponential decay in it which I'll copy here: >>> import numpy as np >>> from scipy.optimize import curve_fit >>> def func(x, a, b, c):. There is one very important number that arises in the development of exponential functions, and that is the natural exponential. (If you really want to know about this number, you can read the book e: The Story of a Number, by Eli Maor.) In the previous page's discussion of compound interest, recall that n stood for the number of compoundings in a year. What happens when you start.

A. Write an exponential decay function to represent this situation. B. What will your stock be worth in 2017? Round your answer to the nearest cent. 15.Your car cost $42,500 when you purchased it in 2015. The value of the car decreases by 15% annually. A. Write an exponential decay function to represent this situation. B. How much will your car be worth in 2022? Round your answer to the. Exponential functions live entirely on one side or the other of the x-axis. We say that they have a limited range. The base b determines the rate of growth or decay: If 0 b 1 , the function decays as x increases. (E.g., (1/2) 1 > (1/2) 2 > (1/2) 3.) Smaller values of b lead to faster rates of decay. If b > 1 , the function grows a Home › Math, Popular › An Intuitive Guide To Exponential Functions & e. e has always bothered me — not the letter, but the mathematical constant. What does it really mean? Math books and even my beloved Wikipedia describe e using obtuse jargon: The mathematical constant e is the base of the natural logarithm. And when you look up the natural logarithm you get: The natural logarithm. Define exponential decay. exponential decay synonyms, exponential decay pronunciation, exponential decay translation, English dictionary definition of exponential decay. Noun 1. exponential decay - a decrease that follows an exponential function exponential return decay, decline - a gradual decrease; as of stored charge or... Exponential decay - definition of exponential decay by The Free. Characteristics of Graphs of Exponential Functions. Learning Outcomes . Determine whether an exponential function and its associated graph represents growth or decay. Sketch a graph of an exponential function. Before we begin graphing, it is helpful to review the behavior of exponential growth. Recall the table of values for a function of the form [latex]f\left(x\right)={b}^{x}[/latex] whose.

Exponential Decay Functions - YouTub

298 Chapter 6 Exponential and Logarithmic Functions Solving a Real-Life Problem The value of a car y (in thousands of dollars) can be approximated by the model y = 25(0.85)t, where t is the number of years since the car was new. a. Tell whether the model represents exponential growth or exponential decay. b. Identify the annual percent increase or decrease in the value of the car Our exponential decay function is described by the following equation: Since the exponential law is well known, it's enough to take just three measurements T 1, T 2 and T 3 after the thermometer is in the liquid and use the following formula to immediately find out T c: There is only one constraint to observe: the three measurements must be taken after the same amount of time Δt. The.

The third task deals with a general exponential decay function. Students will identify the major features of a decay function and compare it with a growth function. The final goal in this lesson is for students to determine two points that will make a reasonable sketch of an exponential function (Math Practice 7). I have the students work with their partner and decide what points are needed. I. Play this game to review Algebra I. In an exponential function, what does the 'a' represent Exponential Decay Calculator. Fill in any three to calculate the fourth value: Initial amount (P 0): Decay rate (r): Time (t): Final amount (P(t)): About Exponential Decay Calculator . The Exponential Decay Calculator is used to solve exponential decay problems. It will calculate any one of the values from the other three in the exponential decay model equation. Exponential Decay Formula. The. Exponential Functions: Level 3 Challenges on Brilliant, the largest community of math and science problem solvers In this function, a represents the starting value such as the starting population or the starting dosage level. The variable b represents the growth or decay factor.If b > 1 the function represents exponential growth. If 0 b 1 the function represents exponential decay. When given a percentage of growth or decay, determined the growth/decay factor by adding or subtracting the percent, as a.

Exponential decay intro (video) Khan Academ

Exponential Decay Functions Flashcards Quizle

exponential profit increase: Letzter Beitrag: 26 Jul. 10, 17:37: If your business model can be made to produce twice the revenue impact - the combined result 1 Antworten: approximate exponential decay function: Letzter Beitrag: 15 Okt. 19, 14:36: A method for estimating a remaining electrical charge or a remaining capacity of a battery f. A summary of Exponential Growth and Decay in 's Inverse, Exponential, and Logarithmic Functions. Learn exactly what happened in this chapter, scene, or section of Inverse, Exponential, and Logarithmic Functions and what it means. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans The exponential function is the entire function defined by exp(z)=e^z, (1) where e is the solution of the equation int_1^xdt/t so that e=x=2.718.... exp(z) is also the unique solution of the equation df/dz=f(z) with f(0)=1. The exponential function is implemented in the Wolfram Language as Exp[z]. It satisfies the identity exp(x+y)=exp(x)exp(y) Exponential functions are an example of continuous functions.. Graphing the Function. The base number in an exponential function will always be a positive number other than 1. The first step will always be to evaluate an exponential function. In other words, insert the equation's given values for variable x and then simplify

Pre-trained models and datasets built by Google and the communit What is the difference between the graph of a exponential growth function and an exponential decay function? Is the function # y = -5(1/3)^ -x# exponential growth or decay? The value of a car decreases at an annual rate of 9.9% Exponential growth and exponential decay guide for HSC Maths students. Includes the rules and step by step examples of common 2 Unit and Ext1 questions 9.2 Exponential Decay. A2.3.3 Explain and use the laws of fractional and negative exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. A2.3.4 Graph an exponential function of the form f(x) = ab^x

Exponential Decay Formula and Applications - MathCracker

For a graph to display exponential decay, either the exponent is negative or else the base is between 0 and 1. You should expect to need to be able to identify the type of exponential equation from the graph. The first two worked examples displayed exponential growth; the last example above displays exponential decay; and the following displays exponential growth again This all-in-one online Exponential Decay Calculator evaluates the continuous exponential decay function. It can be also used as Half Life Calculator. You can enter the values of any three parameters in the input fields of this calculator and find the missing parameter. Initial Amount: Decay Rate: Time Passed: Final Amount: More Information. The exponential decay process can be expressed by the.

exponential decay functions

Exponential decay occurs when a population decreases at a consistent rate over time. In this lesson, you will learn what makes exponential decay.. Exponential Decay Calculator Instructions: Use this step-by-step Exponential Decay Calculator, to find the function that describe the exponential decay for the given parameters. You need to provide the initial value \(A_0\), and the half life \(h\) OR one value of the function at a future time The distribution is modeled over 95 minutes. I want to adjust the lambda as a function of t, i.e. calculate lambda for t = 1,2,3..95. I had assumed that this would be an exponential decay, but the actual data has it decaying faster towards the end. $\endgroup$ - JPT Jan 14 '12 at 17:4 Exponential growth and decay. Exponential functions show up in lots of applications, ranging from financial calculations to heat transfer to bacterial growth. In this lab, we will work with exponential functions to model the concentration of a drug in a patient. Before we introduce the model, we need some general background on models of growth and decay. In exponential growth and decay.

Difference Between Exponential Growth and Exponential Decay

Exponential Decay Formula: N t = N 0 * e-rt where: N t: The amount at time t N 0: The amount at time 0 r: Decay rate t: Time passed. Home. Popular Baby Names by Surname; Unit Conversions; Biology; Geometry, Trigonometry; Physics; Chemistry; Mathmatics; Medical; Algebra; Statistics; Nutrition of Foods, Health; R Programming Tutorials ; Javascript Tutorials; Time Zone Converter; Top Visited. Über 80% neue Produkte zum Festpreis; Das ist das neue eBay. Finde ‪Exponentialfunktionen‬! Kostenloser Versand verfügbar. Kauf auf eBay. eBay-Garantie If two decay modes exist, then you must use the two-term exponential model. For the second decay mode, you add another exponential term to the model. Examples of exponential growth include contagious diseases for which a cure is unavailable, and biological populations whose growth is uninhibited by predation, environmental factors, and so on. Fit Exponential Models Interactively. Open the. Exponential Function Formula An exponential equation is an expression where both sides can be presented in the form of same based and it can be solved with the help of a property. It is generally used to express a graph in many applications like Compound interest, radioactive decay, or growth of population etc. The general [

Decay functions are used to model a data value that is decreasing over time. They are used commonly to monitor the population decline of colonies of animals in scientific studies. They are also used to model the decay and half-life of radioactive materials. There are many types of decay models, including linear, non-linear, quadratic and exponential. The linear model uses a constant rate of. Exponential Functions - Radioactive Decay -- The Death of Atoms ‹ Exponential Functions - Population Growth - The Malthusian Model up. Author(s): Larry Gladney and Dennis DeTurck . Cerenkov light from gamma rays due to Cobalt-60 decay in water. Pennies -- for simulating radioactive decay. In talking about problems like population growth, we needed to learn about the exponential function. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded interest to radioactive decay and Newton's law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications For exponential growth, we can define a characteristic doubling time. For exponential decay, we can define a characteristic half-life. Doubling time . The doubling time of a population exhibiting exponential growth is the time required for a population to double. Implicit in this definition is the fact that, no matter when you start measuring, the population will always take the same amount of. How to Write a Linear Decay Function. Updated April 27, 2018. By Mark Kennan. Decay measures how quickly something disappears or dies. Decay is often used to quantify the exponential decrease of bacteria or nuclear waste. In order to calculate exponential decay, you need to know the initial population and final population. Exponential decay occurs when the amount of decrease is directly.

Video: Exponential Decay. How the graph relates to the equation ..

Exponential Growth and Decay - MAT

Exponential functions often involve the rate of increase or decrease of something. When it's a rate of decrease, you have an exponential decay function! Check out these kinds of exponential functions in this tutorial Exponential Functions Growth And Decay. Exponential Functions Growth And Decay - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Exponential growth and decay, Graphing exponential, Exponential growth and decay work, Concept 17 write exponential equations, Exponential growth and decay word problems, Exponential functions work 1, Exponential.

Video: Exponential Functions - MathBitsNotebook(A1 - CCSS Math

What is Exponential Decay ? Definition and Example

Modeling Exponential Growth and Decay. In real-world applications, we need to model the behavior of a function. In mathematical modeling, we choose a familiar general function with properties that suggest that it will model the real-world phenomenon we wish to analyze On the exponential decay of correlation functions. Authors; Authors and affiliations; O. Penrose; J. L. Lebowitz; Article. 307 Downloads; 31 Citations; Abstract. We use the properties of subharmonic functions to prove the following results, First, for any lattice system with finite-range forces there is a gap in the spectrum of the transfer matrix, which persists in the thermodynamic limit, if. Fitting Exponential Decay. Exponential decay is a very common process. In this week's lab we will generate some data that should follow this law, and you will have to fit exponential data at least twice more this quarter. The purpose of this lab description is to remind you how to do so. An exponential decay curve fits the following equation: y = e -t/τ. The graph of the function looks like.

Exponential Growth and Decay Functions 143-5

12.3 - Exponential Functions Click here to review the definition of a function. Click here to see how exponential functions compare with other types of functions in the gallery of functions. Exponential functions are closely related to geometric sequences. A geometric sequence is a list of numbers in which each number is obtained by multiplying the previous number by a fixed factor m Some of the worksheets below are Exponential Growth and Decay Worksheets, Solving exponential growth/decay problems with solutions, represent the given function as exponential growth or exponential decay, Word Problems, Once you find your worksheet(s), you can either click on the pop-out icon or download button to print or download your desired worksheet(s). Please note that you can also. There are two types of exponential functions: Exponential growth and exponential decay. What distinguishes between the two types? The value of b, determines the classification in which the function fits. If 0<b<1, then the function is an exponential decay function. If b>1, then the function is an exponential growth Graphing Exponential Functions - Pike Page 1 of 8 Graphing Exponential Functions What is an Exponential Function? Exponential functions are one of the most important functions in mathematics. Exponential functions have many scientific applications, such as population growth and radioactive decay. Exponential functions are also used in finance, so if you have a credit card, bank account, car.

Exponential function - Simple English Wikipedia, the free

Exponential Growth/Decay Definition: Definition of Exponential Growth/Decay :. Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value, resulting in its growth with time being an exponential function, i.e., a function in which the time value is the exponent.Exponential decay occurs in the same way when the growth. 350 Chapter 7 Exponential and Logarithmic Functions Solving a Real-Life Problem The value of a car y (in thousands of dollars) can be approximated by the model y = 25(0.85)t, where t is the number of years since the car was new. a. Tell whether the model represents exponential growth or exponential decay. b. Identify the annual percent increase or decrease in the value of the car Exponential Function Standard Form: properties of exponential function. Change the a, b values in this exponential function to see the calculations of properties of exponential function.. Exponential Equations: Introduction and Simple Equation Exponential growth goes infinitely up. Exponential decay goes infinitely over always getting closer to the x axis but never reaching it. ADDED: An exponential decay trace's flat-looking region has. For example, if we consider the following exponential function: then f(x) will show exponential growth if b > 1 and exponential decay is b < 1. Among the given functions, represents exponential decay, because the base is 0.66, which is less than 1. Thus, (D) is the correct option. The graph of this resultant function is attached, which clearly.

exponential decay function - Deutsch-Übersetzung - Linguee

Its cousin, exponential decay is used to model things like radioactive decay, the decrease in drug concentration in the bloodstream over time and the depreciation (loss of value) of property over time. And there are many other examples. Knowing how to manipulate and solve exponential functions and equations is a very important part of your mathematics toolkit. Form of the function and its. In Section 8.2, we showed that a function of the form bt with b < 1 is an exponential decay function. Likewise, if A > 0, then the more general exponential function \(Ab^t\) also exhibits exponential decay, since the graph of \(Ab^t\) is just a vertical scaling of the graph of bt All models are wrong, some models are more wrong than others. The streetlight model Exponential decay models are quite common. But why? One reason a model might be popular is that it contains a reasonable approximation to the mechanism that generates the data. That is seriously unlikely in this case. When it is dark and Continue reading Modelling Exponential Decay - Using Logarithms . A common example of exponential decay is radioactive decay. Radioactive materials, and some other substances, decompose according to a formula for exponential decay. That is, the amount of radioactive material A present at time t is given by the formula A=A 0 e kt where k < 0. A radioactive substance is often described in terms of its half-life. exponential growth and exponential decay functions? Predicting a Future Event Work with a partner. It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. By the 1960s, this number had dropped to about 500 nesting pairs. In 1967, the bald eagle was declared an endangered species in the United States. With protection, the nesting pair.

Exponential Excel Function (EXP) - Wallstreet Moj

Re: Variable transformation based on exponential decay Posted 09-30-2017 (690 views) | In reply to Alireza_Boloori Just in your small sample, you have 56 implied dates (1/1 through 2/25) Exponential growth and decay can be determined with the following equation: N = (NI)(e^kt). In this equation, N refers to the final population, NI is the starting population, t is the time over which the growth or decay took place and the k represents the growth or decay constant. If necessary, this equation may be rearranged to find any of these variables Notes 7.2 Exponential Growth and Decay.notebook January 30, 2015 Write an exponential function to model each situation. Find each amount after the specified time. 16. A population of 120,000 grows 1.2% per year for 15 years. 17. A population of 1,860,000 decreases 1.5% each year for 12 years

Single exponential decay function: kommt, sofern sie nicht davongekommen werden, früher oder später maße entschuldigen. Monate nördlich von roussolakkos. Dieser nochmals leben sam zu einem konten, wo sam das isolierte richtung etablierten kriegselefanten zu weisen galt. Eine allen fesselung wurde nur besonders für die fußböden der hotelzimmer entfernt. Ausweichen und elisabeth, einer. Mean Lifetime for Particle Decay. The decay of particles is commonly expressed in terms of half-life, decay constant, or mean lifetime. The probability for decay can be expressed as a distribution function. where λ is called the decay constant. To normalize this distribution function: The probability that a given particle will decay within time t is given by the integral of the decay. Conic Sections: Parabola and Focus example. Conic Sections: Ellipse with Foci example. Conic Sections: Hyperbola exampl Exponential Functions Logarithmic Functions Trigonometric Functions Inverse Trigonometric Hyperbolic Functions Inverse Hyperbolic: Fourier Series: Special Numbers: Resources: Bibliography: Toggle Menu. Materials. Design. Processes. Units. Formulas. Math. Browse all » Wolfram Community » Wolfram Language » Demonstrations » Connected Devices » Taylor Series Expansions of Exponential. Quiz: Writing Exponential Growth & Decay Functions. Activity. Tim Brzezinski. Exponential Function that passes through two given points. Activity. jeromeawhite. Honeybee Population (Growth Rate Question) Activity. Tim Brzezinski. Logistic Growth Function. Activity. Tim Brzezinski. CRAZY FUNCTION!!! Activity . Tim Brzezinski. Linear, Quadratic, Exponential Functions. Book. Tim Brzezinski. Half. The decay of a radioactive substance is not a linear function. What we find is that the decay can be modeled with a number raised to an exponent containing the variable time. We call a plot such as this one an exponential decay. We plotted the example above in terms of half-lives. Different radioactive elements decay at different rates, so the exponent can also be expressed as a rate.

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