Question

The largest population the forest can sustain is represented mathematically by the limit as t approaches infinity. Determine this limit.
P(t)= 20/ 1+3e^(-0.02t)
where p is squirrel population in hundreds, and t is time in weeks

Answer 1

so, I definitely hope this will be true- well , I am just a student:\[\lim_{t \rightarrow \infty}\frac{ 20 }{ 1+ 3e ^{-0.02t} }\]

=\[\lim_{t \rightarrow \infty}\frac{ 20(1-3e ^{-0.02t}) }{ (1+3e ^{-0.02t})(1-3e ^{-0.02t}) }\]
=\[\lim_{t \rightarrow \infty}\frac{ 20-60e ^{-0.02t} }{ 1-9e ^{-0.04t} }\]
=

\[\lim_{t \rightarrow \infty}\frac{ 20- 0 }{ 1-0 } =20\]

this is so because \[3e ^{-0.02t }= \frac{ 3 }{e ^{-0.02t} }\]

and as t gets to infinity, the whole expression becomes zero. The same goes for the denominator

Answer 2

Yup thats right thanks for helping :)

Answer 3

hey, am so happy!