Model Exponential Growth and Decay
Solve.
-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 700 pounds of the material are placed in the vault, how much time will need to pass for only 231 pounds to remain?
A) 160 years
B) 165 years
C) 170 years
D) 320 years

Question

Quizplus · Accepted Answer

To find the time $x$ when the amount of material is 231 pounds, substitute $A = 231$ and $A_0 = 700$ into the given equation and solve for $x$: $231 = 700e^{-0.00693x}$. Solving this equation for $x$ gives approximately 160 years.

Model Exponential Growth and Decay Solve A=A0e−0.00693x\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.00693 \mathrm { x } }A=A0​e−0.00693x

Model Exponential Growth and Decay
Solve $\mathrm { A } = \mathrm { A } _ { 0 } \mathrm { e } ^ { - 0.00693 \mathrm { x } }$