Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Half-Life } \
\text { (in years) }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 500 & 15 & 45 &
\end{array}$

A) $157.5$
B) $1687.5$
C) $62.5$
D) 250

Question

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Half-Life } \
\text { (in years) }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 500 & 15 & 45 &
\end{array}$

A) $157.5$
B) $1687.5$
C) $62.5$
D) 250

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 number of years, and $T$ is the half-life in years. Plugging in the given values: $A = 500(1/2)^{45/15} = 500(1/2)^3 = 500(1/8) = 62.5$.

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