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Answer:
a) 30.7 million
b) 1.5% per year
c) 42.0 million
d) 2017
Explanation:
a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.
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b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.
The population is growing by 1.5% per year.
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c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.
P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0
The population in Canada in 2021 is predicted to be 42.0 million.
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d) For this we need to solve for t when P(t) = 40.
40 = 30.7·1.015^t
40/30.7 = 1.015^t
Taking logarithms gives ...
log(40/30.7) = t·log(1.015)
t = log(40/30.7)/log(1.015) ≈ 17.773
In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.
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Additional comment
The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.