Answer
$k=-\dfrac{\ln10000}{15}\approx-0.614023$
Work Step by Step
$e^{-15k}=10000$
Apply $\ln$ to both sides of the equation:
$\ln e^{-15k}=\ln10000$
Take $-15k$ down to multiply in front of its $\ln$:
$-15k\ln e=\ln10000$
Since $\ln e=1$, this equation becomes:
$-15k=\ln10000$
Solve for $k$:
$k=-\dfrac{\ln10000}{15}\approx-0.614023$