# How do you solve 50=600e^(-0.4x)?

Jan 19, 2016

First, isolate the exponential function ...

#### Explanation:

$50 = 600 {e}^{- 0.4 x}$

${e}^{0.4 x} = 12$

Now, take the natural log of both sides ...

$\ln \left({e}^{0.4 x}\right) = \ln 12$

$0.4 x = \ln 12$

$x = \frac{\ln 12}{0.4} \approx 6.2123$

hope that helped!