Question

The function A = Ape-0.0099x models the amount in pounds of a particular radioactife material stored in a concrete vault, where x is the numberof years since the material was put into the vault. How many years will it be until 30% of the original amount remains in the vault? Round off tothe nearest year.

Answer 1

we have the following equation:

`A=A_pe^(-0.0099x)`

For this case we can do this:

`0.3A_p=A_pe^(-0.0099x)`

We can cancel in both sides Ap and then we can apply natural log and we got:

`\ln (0.3)=-0.0099x`

Solving for x who represent t we got:

`x=(\ln (0.3))/(-0.0099)=121.61`

Rounded to the nearest year we got:

121yr