Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\text { Original } & \text { Half-Life } \
\text { Amount } & \text { (in years) } & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 400 & 8 & 52 &
\end{array}$

A) $4.4$
B) $1.6$
C) $425.7$
D) $359.5$

Question

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\text { Original } & \text { Half-Life } \
\text { Amount } & \text { (in years) } & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 400 & 8 & 52 &
\end{array}$

A) $4.4$
B) $1.6$
C) $425.7$
D) $359.5$

Quizplus · Accepted Answer

The exponential decay formula is $A = P(1/2)^{t/T}$, where $A$ is the final amount, $P$ is the original amount, $t$ is the time elapsed, and $T$ is the half-life period. Plugging in the given values: $A = 400(1/2)^{52/8} = 400(1/2)^{6.5} \approx 4.4$.

Use the Exponential Decay Formula with Half-Lives to Find the Final