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Sagot :
Part a: Time taken to double the population of chipmunks is 5/2 months.
Part b: Population at population size; P = 200 is 50.
Explain the term average rate of population change?
- 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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