Answer
$B=500e^{-0.4581t}$
Work Step by Step
$B=B_0a^{kt}$
Make $a=e$:
$B=B_0e^{kt}$
When $t=0$ (in the beginning) $B=500$:
$500=B_0e^{k·0}=B_0e^0$
$500=B_0(1)$
$B_0=500$
When $t=2$ (two hours later) $B=200$:
$200=500e^{k·2}$
$\frac{200}{500}=e^{2k}$
$e^{2k}=0.4$
$\ln e^{2k}=\ln0.4~~$ (Use the Inverse Property: $\ln e^x=x$):
$2k=\ln0.4$
$k=\frac{\ln0.4}{2}=-0.4581$
Finally we have:
$B=500e^{-0.4581t}$
