Solve the problem.
-The function $\mathrm { A } = \mathrm { A } _ { \mathrm { o } } \mathrm { e } ^ { - 0.0099 \mathrm { t } }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where t is the number of years since the material was put into the vault. If 900 pounds of the
Material are placed in the vault, how much time will need to pass for only 204 pounds to remain? Round to the
Nearest year.
A)155 yr
B)300 yr
C)150 yr
D)160 yr

Question

Quizplus · Accepted Answer

Given the equation $A = A_0 e^{-0.0099t}$ and the initial amount $A_0 = 900$ pounds, we want to find the time $t$ when $A = 204$ pounds. Substituting these values into the equation gives $204 = 900e^{-0.0099t}$. Solving for $t$ involves dividing both sides by 900, taking the natural logarithm of both sides, and then solving for $t$, which results in approximately 150 years.

Solve the Problem A=Aoe−0.0099t\mathrm { A } = \mathrm { A } _ { \mathrm { o } } \mathrm { e } ^ { - 0.0099 \mathrm { t } }A=Ao​e−0.0099t

Solve the Problem $\mathrm { A } = \mathrm { A } _ { \mathrm { o } } \mathrm { e } ^ { - 0.0099 \mathrm { t } }$