Answer
The half-life of radium-226 is about 1612 years.
Work Step by Step
$$
\begin{aligned}
\frac{1}{2} A_{0} &=A_{0} e^{-0.00043 t} \\
& \quad\left[\begin{array}{c}{ \text {Divide by } A_{0}} \end{array}\right] \\
\frac{1}{2} &=e^{-0.00043 t} \\
& \quad\left[\begin{array}{c}{ \text {Take ln of both sides} } \end{array}\right] \\
\ln \frac{1}{2} &=-0.00043 t \\
-\ln 2 &=-0.00043 t \\
t &=\frac{\ln 2}{0.00043} \\
t & \approx 1612
\end{aligned}
$$
The half-life of radium 226 is about 1612 years.
