# Exponential decay

• Jan 28th 2010, 08:58 AM
arandomnerd
Exponential decay
The decay of a radioactive substance is governed by the relation

N = Pe^(-kt)

where P is the amount at time t=0
N is the amount at time t
k is the decay constant

For a certain substance 14% has decayed in 23 years, calculate the half life of the substance.
How long will it take 44% of the substance to decay?

• Jan 28th 2010, 10:05 AM
Black
Quote:

Originally Posted by arandomnerd
For a certain substance 14% has decayed in 23 years, calculate the half life of the substance.

So we have

$N(23)=.86P=Pe^{23k}$.

Solve for $k$. To find the half-life $t_{1/2}$, we have

$.5P=Pe^{kt_{1/2}} \Longrightarrow t_{1/2}=\frac{\text{ln}(1/2)}{k}$.

Quote:

Originally Posted by arandomnerd
How long will it take 44% of the substance to decay?

Solve for t in the equation

$.56P=Pe^{kt}$.