ANSWER
To three decimal places,
t ≈ 815.467
EXPLANATION
[tex]\begin{aligned}
\dfrac{1}{2} &= 1 \cdot e^{-.00085\cdot t} \\
\dfrac{1}{2} &= e^{-.00085\cdot t}
\end{aligned}[/tex]
We can use the definition of logarithm to convert this equation into exponential form.
[tex]e^a = b \iff \log_e(b) = a \iff \ln(b) = a[/tex]
therefore,
[tex]\begin{aligned}
\dfrac{1}{2} &= e^{-.00085\cdot t} \\
\ln\left( \tfrac{1}{2} \right) &= -.00085\cdot t \\
t &= \frac{\ln\left( \tfrac{1}{2} \right)}{-.00085} \\
t &\approx 815.467
\end{aligned}[/tex]
