Question

The function P(n) = 10*2^n/4 models the population of tree frogs living in a park after n months. How many months will it take for the tree frog population to reach 5120? Show your work.

Answer 1

They've given us a P value, so we just need to plug it into our function and find the corresponding n value:
$5120=10(2^{\frac{n}{4}})$
$512=2^{\frac{n}{4}}$

Then take the natural log of both sides:
$\ln(512)=\ln(2^{\frac{n}{4}})=\frac{n}{4}\ln(2)$
$\frac{\ln(512)}{\ln(2)}=\frac{n}{4}$
$4*\frac{\ln(512)}{\ln(2)}=n$

Putting this into a calculator:
$n=36$