Solve the problem.
-The function $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.00693 \mathrm { x } }$ 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 800 pounds of the material are placed in the vault, how much time will need to pass for only 492 pounds to remain?
A) 70 years
B) 75 years
C) 80 years
D) 140 years

Question

Quizplus · Accepted Answer

To find the time $x$ when 492 pounds remain, use the equation $492 = 800 \cdot e^{-0.00693x}$. Solving for $x$, we get $x = \frac{\ln(492/800)}{-0.00693} \approx 70$ years.

Solve the Problem A=A0e−0.00693x\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.00693 \mathrm { x } }A=A0​e−0.00693x

Solve the Problem $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.00693 \mathrm { x } }$