A herd of 20 white-tailed deer is introduced to a coastal island where there had

Question

A herd of 20 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to the logistic curve

A=100/1+4e^(-0.14t)

where A is the number of deer expected in the herd after t years

A) How many deer will be present after 2 years? After 6 years? Round answer to the nearest integer.

B) how many years will it take for the herd to grow to 50 deer? Round answer to the nearest integer.

C) Does A approach a limiting value as i increases without bound?

Explanation / Answer

A.

A(2)=100/(1+4e-0.14(2))=24.9

A(6)= 100/(1+4e-0.14(6))=36.7

B. 50=100/(1+4e-0.14t)

1+4e-0.14t=2

e-0.14t=1/4

t=9.9

C. As t approaches to infinity,A approches to 100 .

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