Answer
$x\approx277.26$
Work Step by Step
Divide by $400$ on both sides. Then use the natural log on both sides, and then solve for $x$.
$400e^{0.005x}=1600$
$e^{0.005x}=4$
$\ln e^{0.005x}=\ln4$
$0.005x=\ln4$
$x=\frac{\ln4}{0.005}$
$x\approx277.26$
