Question

The function A = Age-0.0099x 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 700 pounds of the material are initially put
into the vault, how many pounds will be left after 170 years?

Answer 1

130.06pounds

Explanation:

Given the function
`A = A_ge^(-0.0099x)` that 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 and Ag is the initial amount in pounds.

If 700 pounds of the material are initially put into the vault, the amount of pounds left after 170years can be expressed as shown;

`A = 700e^(-0.0099(170)) \where\ Ag = 700years\ and\ x = 170years\\A = 700e^(-1.683)\\A = 700*0.1858\\A = 130.06 pounds`

The amount of pounds of radioactive material that will be left after 170years is approximately 130pounds