Question

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 the material are initially put into the vault, how many pounds will be left after 140 years?

Answer 1

Amount = 500 e^(-.01386(140))
= 71.823

(my keystrokes on my calculators are as follows:
2nd F
ln
(
.01386
±
x
140
)
=
x
500
=

Answer 2

the 500 pounds represent the Ao in the equation (Ao is the initial amount),, since there is time given (x = 140 years), we can substitute the values directly:
A = Ao*e^(-0.01386x)
A = (500)*e^(-0.01386*140)
A = ?
now plug in these values in calculator and you'll get A~

hope this helps~ :)