Answer
The half-life of plutonium-241 is about 13 years.
Work Step by Step
$$
\begin{aligned}
\frac{1}{2} A_{0} &=A_{0} e^{-0.053 t} \\
& \quad\left[\begin{array}{c}{ \text {Divide by } A_{0}} \end{array}\right] \\
\frac{1}{2} &=e^{-0.053 t} \\
& \quad\left[\begin{array}{c}{ \text {Take ln of both sides} } \end{array}\right] \\
\ln \frac{1}{2} &=-0.053 t \\
-\ln 2 &=-0.053 t \\
t &=\frac{\ln 2}{0.52} \\
t & \approx 13
\end{aligned}
$$
The half-life of plutonium-241 is about 13 years.
