Question

radioactive decay question??

The rate of decay of a radioactive substance is proportional to the amount present. Four years ago there were 12 grams of substance. Now there are 8 grams. How many grams will there be 8 years from now?

Answer 1

Please help!

Answer 2

The amount four years ago is determined by the equation
\[N _{t}=N _{0}e ^{-kt}=12\ .............(1)\]
The amount now is determined by the equation
\[N _{t+4}=N _{0}e ^{-k(t+4)}=8\ .........(2)\]
Dividing equation (1) by equation (2) gives
\[\frac{e ^{-kt}}{e ^{-k(t+4)}}=\frac{12}{8}\]
from which we get
\[e ^{4k}=1.5\]
When you solve for the decay constant k, you can set up another pair of equations for the weight now and the weight 8 years from now and solve for the weight in 8 years.