What is Exponential decay: Definition and 41 Discussions

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant:





{\displaystyle {\frac {dN}{dt}}=-\lambda N.}
The solution to this equation (see derivation below) is:







{\displaystyle N(t)=N_{0}e^{-\lambda t},}
where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0, and the constant λ is called the decay constant, disintegration constant, rate constant, or transformation constant.

View More On Wikipedia.org
  1. aspodkfpo

    How does this exponential decay formula get derived?

    https://www.asi.edu.au/wp-content/uploads/2015/03/PhysicsASOE2013soln.pdf Q12 e) Working backwards, P = Ae^kt form, i.e. EAts = Emin e^(ln2/τ x t). Not sure how they get this formula in the first place with these values.
  2. B

    Investigating the Impact of Heating a Substance on Room Temperature

    Through the research that I conducted is that I wasn't able to find actual supporting answer to this question. I struggle with Physics and math and because of Coronavirus my school has shut down meaning I don't have access to my teachers or tutor. The main line that i am thinking is that if it...
  3. J

    B Deriving Exponential Decay Equation

    Hi, I was trying to see where the equation N = No e-λt came from and it is derived from dN/dt = -λN which is discussed very well in this thread in post #2 (https://www.physicsforums.com/threads/derivations-of-the-decay-constant-equation.213312/). I understand the steps except for the reason why...
  4. wolf1728

    I What is the exponential decay equation for a bouncing ball?

    This is not a physics question. Each time a ball bounces it will bounce to, let's say 75% of its previous height. (I am not interested in the time, energy or velocity, of the ball.) So if we drop it from 100 cm it will bounce back up to 75 cm, and on the next bounce it goes up to 56.25 cm and...
  5. A

    Exponential decay of a pendulum oscillation amplitude

    Homework Statement I found an answer on the internet for this problem, but I'm not sure on one of the steps. The solution says, "Take ln of both sides to get rid of Ae. If we do that, then the right side will be ln(Ae^t/T). I don't see how using ln will get rid of Ae? Homework Equations Refer...
  6. R

    B Exponential decay convolved with Gaussian

    Hello all, I have a data which look like reversed exponentially modified Gaussian (EMG) function and interested to fit the data with with reversed EMG function. After searching on internet I found the EMG function, which is given below...
  7. Jehannum

    I Exponential decay: I need an expression for N at time t

    I have a large quantity N, which starts off equal to a determinable value N0. Over a short time ∆t, the value of N changes by -∆t*(B*N - C) where B and C are determinable constants. Am I correct in thinking I can turn this into: dN/dt = -(B*N - C) How do I get this into a formula for N at...
  8. Y

    How Long Until Superman Regains His Powers?

    Homework Statement superman has been disabled by a nearby amount of kryptonite, which decays exponentially. If Superman cannot regain his power until 90% og the kryptonite disintegrates, then how long will it be before he regain his powers? Use r=-0.138629. Round to the nearest day. a. 4days...
  9. S

    Creating an Exponential decay equation for given parameters

    So, I am wanting to vary a parameter in an equation with respect to time. Vary mass flow [ m(t) ] for an exponential decay to half its original value in around 60 seconds. I know the regular decay equation where: m(t)=m0*exp(-At) but I want the value to approach a steady state at 60 seconds...
  10. P

    MHB Calculating Time for Iodine 131 to Decay to 5% of Initial Dose

    So i have a graph representing iodine 131 y axis of 0-100 iodine remaining in the body (%of dose) x asis 0-60 Time in days with the points plotted (24,12.5) The equation of the graph is D = D0 (b) t/k So i have figured out "k" which is 8 for iodine half life. Which it asked me to do in the...
  11. S

    Tunneling from Rectangular barrier - Exponential Decay ?

    Tunneling from Rectangular barrier - Exponential Decay ?? Consider the Rectangular Potential Barrier. If one solves bound state Problem in this case, wavefunctions of Exponentially Decaying and rising kind are found for the Region in the Barrier. ψ = A eαx + B e-αx Yet Most Books and...
  12. C

    Poisson distribution & exponential decay

    Homework Statement t(s) = 1 15 30 45 60 75 90 105 120 135 N(counts) = 106 80 98 75 74 73 49 38 37 22 Consider a decaying radioactive source whose activity is measured at intervals of 15 seconds. the total counts during each period are given. What is...
  13. B

    Exponential Decay function in NMR

    Homework Statement How many oscillations occur before Mxy decays to approximately 1/3 of its initial value, for a Larmor frequency of 100 MHz and T2 of 100ms?Homework Equations I was learning about how NMR works and about transverse relaxation. According to what I learned, we can express...
  14. F

    Exponential decay and half life problem

    the half life of C14 is 5730 years. if a sample of C14 has a mass of 20 micrograms at time t = 0, how much is left after 2000 years? I learned from somewhere that these exponential decay and half life problems use the equation y = ab^t or y = a(1+r)^t where y = total, a = initial...
  15. B

    Functions that exhibit exponential decay behavior?

    Any help is appreciated, thanks. Homework Statement In my course of differentials equations we were given the task to model a real life system with them, we choosed something that resembles a pendulum.Homework Equations The Attempt at a Solution We went to the lab and got experimental data from...
  16. DeusAbscondus

    MHB What are some common traps to watch out for in word problems?

    Hi folks could someone please check my calculations contained in attached file? thanks. (incidentally, how can i create a link to such files in the future, weaving them into my text?) Deus(has gone)
  17. J

    Dead bodies - exponential decay

    Homework Statement A body is found at 2:00pm at a temperature of 26°C, with a surrounding temperature of 18°C. Two hours later the temperature of the body is 21°C, when did the body die? T=Ae^(kt)+Ts where T is the temperature of the body A is the initial temperature k is a constant t...
  18. MarkFL

    MHB Abby's question at Yahoo Answers involving exponential decay

    Here is Abby's question: Here is a link to the original question: Differential Equations time constant problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  19. T

    Question about exponential decay timing.

    I'm trying to understand the concept of exponential decay. To clarify, the decay of Uranium is not the same as say pulling the plug in a tub full of water. The water will drain out of a tub at a steady rate from start to finish. I assume Uranium doesn't do that. So you COULD say the water has a...
  20. P

    Exponential decay, but results reach 0

    So I have a situation where the results in a table (x and y), where y reaches 0. According to my understanding, mathematically, exponential decay can never reach 0, right? So does that mean that I can't use an exponential curve of best fit with the results in my table (x = 0,1,2,3), (y = 4...
  21. K

    Exponential Decay with Matrices

    Homework Statement 6. Three disease-carrying organisms decay exponentially in seawater according to the following model: P(t) = Ae-1.5t + Be-0.3t + Ce-0.05t t 0.5, 1, 2, 3 , 4, 5, 6, 7, 9 p(t) 6, 4.4, 3.2, 2.7, 2, 1.9, 1.7, 1.4, 1.1 Estimate the initial concentration of each...
  22. X

    Fast fourier transform on exponential decay function

    Hi all: I have one confused question. one continuous exponential decay function f=exp(-lamda*t) start from t=0 to infinity. I sample 1024 data points from the decay function. time variable (t) ranges from 0 to 1 second. the tail data of this exponential function is zero. I apply discret FFT on...
  23. O

    Quick question on exponential decay problem

    I'm attaching the problem as a png. The top half is the question whereas the second half is the solution. I understand everything about the question until the ultimate answer the final answer is: (r (constant) x0(constant) / k (constant)) * (1 - e^-60t) as shown. However I don't...
  24. A

    Question on exponential decay?

    Hi everyone, There's something that's kind of been bugging me about applying exponential decay formulas to real world phenomena. For example let's say the discharging of a parallel plate capacitor. Let's consider the negative plate. As it discharges excess electrons leave the plate. The...
  25. L

    How Do Lambda and Beta Relate in the Exponential Decay of Foam?

    Hello, Suppose you observe some foam. The foam is formed by a set of bubbles, and each bubble blows up after a random time. The density function of the time each bubble will take to blow up is probably exponential, with rate lambda. The total amount of foam (Q) must also decay exponentially...
  26. R

    Exponential decay question. fundamental

    this is just something has been bugging me for the last few days. it seems like it has a very basic solution. Muons decay randomly, but have a mean lifetime of about 2 us. If I plot the # of muons that decay vs. time (say the axis spans from 0 to 20 us), why is the plot exponential decay...
  27. H

    Exponential Decay Homework: Solving 8 mg After 100 Years

    Homework Statement A radioactive substance has a half-life of 20 years. If 8 mg of the substance remains after 100 years, find how much of the substance was initially present. Homework Equations A=A0ekt The Attempt at a Solution I set the equation up so that 8=A0e100k and...
  28. M

    Exploring Exponential Decay in Light Absorption

    Hi I'm self-teaching calculus and I'm looking at exponential growth and decay. The differential equation for relationships like these if this was related to time is dP/dt = -kP i.e. the rate of change in P with time decreases at a rate which is proportional to the amount of P present. I can...
  29. N

    Effective half-life multiple exponential decay

    Say we have a decay of the form A e^{-a x} + B e^{-b x}. I haven't had much luck trying to calculate the half-life of such a decay (I'm not sure it's possible, analytically), i.e. solve A e^{-a x} + B e^{-b x} = \frac{A+B}{2}. However, if that's not possible, I'm wondering whether...
  30. S

    Differential Equations - Exponential Decay

    Homework Statement We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for...
  31. S

    Understanding the Meaning of 'a' in Exponential Decay Model

    Homework Statement In the standard model for exponential decay, y=ab^x , what does a represent and why? The Attempt at a Solution I know that a is the value of y when x=0, but I don't understand why this is the case. Any help would be appreciated, thanks.
  32. B

    Understanding the Formula for Exponential Decay of Voltage

    Please Help! This is based on the time at any point on the curve during exponential decay of voltage. Could someone explain to me this formula? t=T1n(E/Vl) example: t=(7.5ms)1n(20v/14.57v)=2.38ms. I get 20/14.57=1.372683596 (7.5)(1.372683596)=10.29512697 where and how do...
  33. S

    Why Radioactive Decay is Exponential: A Simple Explanation

    Somewhere the connection is not being made. I have seen all the analogies (flipping pennies, popcorn, etc) and know all the equations. What is the simplest self-contained explanation for why radioactive (ie random) decay is exponential, rather than linear, for example? How do you translate...
  34. P

    Calculating Exponential Decay of Thorium Isotope from Supernova Explosion

    [SOLVED] Exponential decay Homework Statement A certain amount of the radioactive isotope of thorium ^{232}Th was produced during a supernova explosion 2 billion years ago. This isotope decays according to the exponential law N(t) = Noe^{-t/to}, where No and N are the initial number of...
  35. T

    Atmospheric Density, exponential decay derivation

    I've read my lecture notes about 100x but can't even begin to see where this derivation can come from. A previous derivation was the equation dP/dz = -gρ (P = pressure, z = distance, g= acc due to grav, ρ = density) If atmosphere can be treated as an isothermal ideal gas of constant mean...
  36. A

    Solving Exponential Decay: 10,000 Years & Uranium II

    Homework Statement The half life of radioactive Uranium II is about 250,000 years. What percent of radioactive uranium will remain after 10,000 years? Homework Equations The Attempt at a Solution
  37. J

    Exponential decay with air pressure

    Air pressure, P, decreases exponentially with the height, h, in meters above sea level: P = P0e-0.00012h where P0 is the air pressure at sea level. (a) At the top of Mount McKinley, height 6198 meters (about 20,330 feet), what is the air pressure, as a percent of the pressure at sea...
  38. J

    Exponential decay word problem (check work)

    At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by A = 10(0.82)t. (a) What was the intial amount taken? 10 mg (b) What percent of the drug leaves the body each hour? 18% (c) How much of the drug is...
  39. chroot

    Exponential Decay: Solving with Radioactive Half-Lives

    From a member called "Banana": Now I'm trying to do one with radioactive decay. Do you think I would use those same formulas? The only confusing thing is that it's not presented the same. It says that a material decays so that it is 99 percent gone in 6.65 half-lives (so would you double...
  40. C

    Is There an Exponential Decay in Water Levels in a Barrel?

    I'm doing a research about water flowing from a barrel through a small hole. I am trying to proove that there is an exponential relationship between the height level of the water and the time. This basically implies that dh/dt= -kh. In order to do that , I have to prove first that the rate...
  41. C

    Is Water Flow from a Barrel an Example of Exponential Decay?

    I'm doing a research about water flowing from a barrel through a small hole. I am trying to proove that there is an exponential relationship between the height level of the water and the time. This basically implies that dh/dt= -kh. In order to do that , I have to prove first that the...