A population of chipmunks moves into a new region at time t=0 months. At time t (in months), the population size is given by

P(t) = 100[1+0. 3t+(0. 04)t^2].

How long does it take for this population to double its initial size P(0)? Include the units in your answer.

What is the average rate of population change between time t=0 and time t=20? Include the units in your answer.

What is the instantaneous rate of growth of the population when the population size is P=200? Include the units in your answer

the country, region, or geographic area's average yearly rate of change in population size over a certain time period.
It expresses the proportion, usually multiplied by 100, between the annual growth in population size and indeed the overall population for that year.

Part a: Time taken to double the population of chipmunks;

P(t) = 100[1 + (0.3)t + (0.04)t²].

P(0) = 100[1 + 0 + 0] = 100

P(t) = 200 = 100 + 30t + 4t²

4t² + 30t − 100 = 0

2t² + 15t − 50 = 0

(2t − 5)(t + 10) = 0

t = 5/2

It will take 5/2 months population to double its initial size P(0).

Part b: Population at population size; P=200

P'(t) = 0 + 30 + 8t

P = 200 when t = 5/2

P'(200) = 30 + 8(5/2)

P'(200) = 30 + 20

P'(200) = 50

Thus, the instantaneous rate of growth of the population when the population size is P=200 is 50.

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