The function $\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-0.0099 \mathrm{x}}$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $\mathrm{x}$ is the number of years since the material was put into the vault. If 200 pounds of the material are initially put into the vault, how many pounds will be left after 160 years?
A) $44 \mathrm{lb}$
B) $229 \mathrm{lb}$
C) $41 \mathrm{lb}$
D) $148 \mathrm{lb}$

Question

Quizplus · Accepted Answer

The initial amount $A_0$ is 200 pounds. After 160 years, the amount $A$ is calculated as $A = 200 \times e^{-0.0099 \times 160}$. This evaluates to approximately 41 pounds.

The Function A=A0e−0.0099x\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-0.0099 \mathrm{x}}A=A0​e−0.0099x Models the Amount in Pounds of a Particular Radioactive Material

The Function $\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-0.0099 \mathrm{x}}$ Models the Amount in Pounds of a Particular Radioactive Material