Answer
$x \approx 5.5$ miles
Work Step by Step
$P(x) = 14.7e^{-0.21x}$
$4.6 = 14.7e^{-0.21x}$
$\frac{4.6}{14.7} = e^{-0.21x}$
$\ln \frac{4.6}{14.7} = -0.21x$
$x = - \frac{\ln \frac{4.6}{14.7}}{0.21}$
by GDC / calculator
$x = 5.532339...$
$x \approx 5.5$ miles