A graphing calculator is recommended. The rabbit population on a small island is

Question

A graphing calculator is recommended. The rabbit population on a small island is observed to be given by the function P(t) = 130t-0.3t4 + 1100 where t is the time (in months) since observations of the island began. (a) When is the maximum population attained (Round your answer to one decimal place.) months What is the maximum population? (Round your answer to the nearest whole number.) rabbits (b) When does the rabbit population disappear from the island? (Round your answer to one decimal place.) months

Explanation / Answer

a)

P(t) =130t -0.3t^4+1100

Find derivative as

P'(t) = 130 - 1.2t^3

Set P'(t) = 0

130 -1.2t^3 =0

1.2t^3 = 130

t^3 = 130/1.2

t= (130/1.2)^(1/3)

t=4.8 months

Find

P(4.8) =1565 rabbits

b)

P(t) =0

130t -0.3t^4+1100 =0 [ Use graphing calculator ZERO feature]

t= 9.4 months

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