Solve the problem.
-The functio $\mathrm { A } = \mathrm { A } _ { \mathrm { O } } \mathrm { e } ^ { - 0.01386 \mathrm { x } }$ 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 600 pounds of the
Material are placed in the vault, how much time will need to pass for only 99 pounds to remain?
A) 140 years
B) 260 years
C) 135 years
D) 130 years

Question

Quizplus · Accepted Answer

To solve for $x$, we substitute $A = 99$ and $A_0 = 600$ into the equation $A = A_0 e^{-0.01386x}$ and solve for $x$. Rearranging the equation gives $x = \frac{\ln(A/A_0)}{-0.01386}$. Substituting the given values yields $x = \frac{\ln(99/600)}{-0.01386}$, which calculates to approximately 130 years.

Solve the Problem A=AOe−0.01386x\mathrm { A } = \mathrm { A } _ { \mathrm { O } } \mathrm { e } ^ { - 0.01386 \mathrm { x } }A=AO​e−0.01386x

Solve the Problem $\mathrm { A } = \mathrm { A } _ { \mathrm { O } } \mathrm { e } ^ { - 0.01386 \mathrm { x } }$