Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Half-Life } \
\text { (in years) }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 26 & 125 & 800 &
\end{array}$

A) $2.8$
B) 0
C) $0.3$
D) $0.4$

Question

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Half-Life } \
\text { (in years) }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 26 & 125 & 800 &
\end{array}$

A) $2.8$
B) 0
C) $0.3$
D) $0.4$

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. Substituting $P = 26$, $t = 800$, and $T = 125$, we get $A = 26(1/2)^{800/125} = 26(1/2)^{6.4} \approx 0.3$.

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