The function A=A0e^-0.01386x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 500 pounds of material are placed in the vault.

Question

A) How much time will need to pass for only 47 pounds to remain?
B) How much material will be left after 10, 20, and 30 years?

Answer 1

A)
47 = 500 e^(-0.01386x)
take ln of both sides and use log rules
ln 47 = (-0.01386x)ln 500
-0.01386x = ln47/ln500

x =
continue

B)I will do the case of 20 years, you do the other two

A = 500 e^(-0.01386(20))
= 500 e^-.2772
= 500(.7579029..)
= appr 379 pounds

Answer 2

47 = 500 e^(-0.01386x)
e^(-0.01386x) = 47/500
-0.01386x = ln(47/500)
x = ln(0.094)/-0.01386