# radioactive decay word problem

Printable View

• Apr 28th 2010, 03:37 PM
yoman360
After t years, \$\displaystyle 50e^{-0.015t}\$ pounds of a deposit of a radioactive substance remain. The average amount per year not lost by radioactive decay during the second hundred years is
(A) 2.9 lb
(B) 5.8 lb
(C) 7.4 lb
(D) 11.1 lb
(E) none of these

if it helps the answer is B but i need help how to get that answer
• May 3rd 2010, 12:00 AM
CaptainBlack
Quote:

Originally Posted by yoman360
After t years, \$\displaystyle 50e^{-0.015t}\$ pounds of a deposit of a radioactive substance remain. The average amount per year not lost by radioactive decay during the second hundred years is
(A) 2.9 lb
(B) 5.8 lb
(C) 7.4 lb
(D) 11.1 lb
(E) none of these

if it helps the answer is B but i need help how to get that answer

The mass remaining at time \$\displaystyle t\$ is:

\$\displaystyle m(t)=50e^{-0.015t}\$

The amount lost between \$\displaystyle t_1\$ and \$\displaystyle t_2\$ is:

\$\displaystyle M(t_1,t_2)=m(t_1)-m(t_2)\$

So the average loss per year is:

\$\displaystyle A(t_1,t_2)=M(t_1,t_2)/(t_2-t_1)\$

CB