# 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:

d
N

d
t

=

λ
N
.

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

N
(
t
)
=

N

0

e

λ
t

,

{\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.

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1. ### How does this exponential decay formula get derived?

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3. ### B Deriving Exponential Decay Equation

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

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5. ### Exponential decay of a pendulum oscillation amplitude

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6. ### B Exponential decay convolved with Gaussian

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

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8. ### How Long Until Superman Regains His Powers?

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9. ### Creating an Exponential decay equation for given parameters

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11. ### Tunneling from Rectangular barrier - Exponential Decay ?

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

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17. ### Dead bodies - exponential decay

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18. ### MHB Abby's question at Yahoo Answers involving exponential decay

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19. ### Question about exponential decay timing.

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20. ### Exponential decay, but results reach 0

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21. ### Exponential Decay with Matrices

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22. ### Fast fourier transform on exponential decay function

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23. ### Quick question on exponential decay problem

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26. ### Exponential decay question. fundamental

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34. ### Calculating Exponential Decay of Thorium Isotope from Supernova Explosion

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38. ### Exponential decay word problem (check work)

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39. ### Exponential Decay: Solving with Radioactive Half-Lives

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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...