Word problem with limit, average rate of change

[tarynt1]

At a private lake, 200 fish are stocked and the population grows according to the logistic function where t is in months: P(t) = 2000/(1+9e^(-t/3)) . Find the limit of P(t) as t approaches infinity.

At what time is the population growing the fastest? How many fish are there at this time?

What is the average rate of change in the fish population during the first 12 months?

Any help? Thanks! =)

 

[galactus]

Take a look at the equation.

\(\displaystyle \L\\P(t)=\frac{2000}{1+9e^{\frac{-t}{3}}}\)

As t approaches infinity, what does \(\displaystyle e^{\frac{-t}{3}}\) approach?

As t gets larger, e^(-t/3) gets smaller and smaller and smaller.

Therefore, what's it approaching?.

See it?.

 

[tarynt1]

So it ends up being 2000 / (1 + 0) . . . and the limit would be 2000. Thanks!

I'm still confused about the other two questions though.