Asked by something
The population (P) of an island y years after colonization is given by the function
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.
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.
Answers
Answered by
oobleck
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.
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.
Answered by
Bauer Supreme 1s Gloves
Would you gladly please explain to me the curve sketching?
Answered by
oobleck
google is your friend. It will provide you with many examples, illustrations and videos. I'm sure your text also discusses the subject!
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