The rabbit population on a small island is observed to be given by the function

P (t) = 130t - 0.4t4 + 1200

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.)

What is the maximum population? (Round your answer to the nearest whole number.)

(b) When does the rabbit population disappear from the island? (Round your answer to one decimal place.)

... ?

Question

Lillie Santos

Mathematics

30 December, 21:34

The rabbit population on a small island is observed to be given by the function

P (t) = 130t - 0.4t4 + 1200

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.)

What is the maximum population? (Round your answer to the nearest whole number.)

(b) When does the rabbit population disappear from the island? (Round your answer to one decimal place.)

... ?

+3

Answers (1)

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Girl · Answer 1

A.) P (t) = 130t - 0.4t^4 + 1200

The population is maximum when P' (t) = 0

P' (t) = 130 - 1.6t^3 = 0

1.6t^3 = 130

t^3 = 81.25

t = ∛81.25 = 4.3 months.

Maximum population P (t) max = 130 (4.3) - 0.4 (4.3) ^4 + 1200 = 1,622

b.) The rabbit population will disappear when P (t) = 0

P (t) = 130t - 0.4t^4 + 1200 = 0

t ≈ 8.7 months