# The population of rabbits in an area is modeled by the growth equation P(t)=8e^0.26t, where P is in thousands and t is in years. How long will it take for the population to reach 25,000?

Jun 23, 2018

I tried this:

#### Explanation:

Let us set $P = 25$ we get:

$25 = 8 {e}^{0.26 t}$

rearrange:

${e}^{0.26 t} = \frac{25}{8}$

take the natural log of both sides:

$\ln \left[{e}^{0.26 t}\right] = \ln \left[\frac{25}{8}\right]$

simplify:

$0.26 t = \ln \left[\frac{25}{8}\right]$

$t = \frac{1}{0.26} \ln \left[\frac{25}{8}\right] = 4.38 \approx 4.4$ years corresponding to 4 years and 5 months (more or less)