The population (P) of an island y years after colonization is given by the function

Question

P=250/1+4e^-0.01y

c. After how many years was the population growing the fastest?
d. Using Curve Sketching methods, sketch the graph of the function. Make sure that you include all steps, charts, and derivations details.

Answer 1

growing the fastest means P' has a max, and thus P" = 0
P' = 10e^(.01y)/(1+4e^.01y)^2
P" = .1 e^.01y (4-e^.01y)/(1+4e^.01y)^3

So, P' is max when e^.01y = 4

for curve sketching, you know there are horizontal asymptotes at P=0 and y=250.
You can also avoid the calculus stuff by reviewing the properties of Logistic Growth curves.

Answer 2

Would you gladly please explain to me the curve sketching?

Answer 3

google is your friend. It will provide you with many examples, illustrations and videos. I'm sure your text also discusses the subject!