Solve.
-The function $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.0077 \mathrm { x } }$ 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 400 pounds of the material are placed in the vault, how much time will need to pass for only 317 pounds to remain?
A) 30 years
B) 35 years
C) 40 years
D) 60 years

Question

Quizplus · Accepted Answer

Given $A = A_0 e^{-0.0077x}$ and $A_0 = 400$, $A = 317$, solve for $x$: $317 = 400e^{-0.0077x}$. Divide both sides by 400, then take the natural logarithm and solve for $x$, yielding approximately 30 years.

Solve -The Function A=A0e−0.0077x\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.0077 \mathrm { x } }A=A0​e−0.0077x

Solve
-The Function $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.0077 \mathrm { x } }$