Question 1154016
A small lake is stocked with a certain species of fish.
The fish population is modelled by the function {{{P(t) = 10/((1+5e^(-0.8t)))}}} where
 P is the number of fish in hundreds and
 t is measured in months since the lake was stocked. 
After how many months will the fish population reach 500 fish?
:
P is the number of fish in hundreds, therefore 500 fish is 5
{{{5 = 10/((1+5e^(-0.8t)))}}}
multiply both sides by {{{(1+5e^(-0.8t))}}}
{{{5(1+5e^(-0.8t)) = 10}}}
divide both sides by 5
{{{1+5e^(-0.8t) = 2}}}
subtract 1 from both sides
{{{5e^(-0.8t) = 1}}}
divide both sides by 5
{{{e^(-0.8t)) = .2}}}
using nat logs
{{{ln(e^(-.8t)) = ln(.2)}}}
-.8t*ln(e) = ln(.2)
ln of e is 1, find the ln of .2 
-.8t = -1.6094
t = {{{(-1.6094)/-.8}}}
t ~ +2 months