# How do you solve 4e^(0.045t)<1600?

Jul 26, 2017

$t = \frac{200 \ln \left(400\right)}{9}$

#### Explanation:

First, we divide both sides by $4$ to isolate the ${e}^{0.045 t}$.

$\frac{\cancel{4} {e}^{0.045 t}}{\cancel{\textcolor{red}{4}}} = \frac{1600}{\textcolor{red}{4}} = 400$

${e}^{0.045 t} = 400$

To remove the $e$, we take the $\ln$ of both sides: $\ln \left({e}^{a x}\right) = a x$

$\cancel{\ln} \left({\cancel{e}}^{0.045 t}\right) = \ln \left(400\right)$

$0.045 t = \ln \left(400\right)$

Now, we nust divide both sides by $0.045$, $\frac{\cancel{0.045} t}{\cancel{\textcolor{red}{0.045}}} = \ln \frac{400}{\textcolor{red}{0.045}}$

$t = \ln \frac{400}{0.045} = \frac{200 \ln \left(400\right)}{9}$