Answer
\[P = 20000\]
Work Step by Step
\[\begin{gathered}
P = 0.00005\int_0^\infty {t{e^{ - 0.00005t}}dt} \hfill \\
\hfill \\
integrate\,\,\,by\,\,parts \hfill \\
\hfill \\
P = 0.00005\,\,\,\mathop {\lim }\limits_{b \to \infty } \,\,\,\left[ {t\,\left( {\frac{{{e^{ - 0.00005t}}}}{{ - 0.00005}}} \right) - \,\,\,\left( {\frac{{{e^{ - 0.00005t}}}}{{ - {{0.00005}^2}}}} \right)} \right]_0^b \hfill \\
\hfill \\
use\,\,the\,\,ftc \hfill \\
\hfill \\
P = 0.00005\,\,\,\mathop {\lim }\limits_{b \to \infty } \,\,\,\,\left[ {b\,\left( {\frac{{{e^{ - 0.00005b}}}}{{ - 0.00005}}} \right) - \,\left( {\frac{{{e^{ - 0.00005b}}}}{{ - {{0.00005}^2}}}} \right) + \frac{1}{{ - {{0.00005}^2}}}} \right]\, \hfill \\
\hfill \\
{\text{evaluate}}\,\,{\text{the}}\,\,{\text{limit}} \hfill \\
\hfill \\
P = \frac{1}{{0.00005}} \hfill \\
\hfill \\
or \hfill \\
\hfill \\
P = 20000 \hfill \\
\hfill \\
\end{gathered} \]
