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A population is said to grow exponentially if its size at time t is given by P(t) = Poe', Where P0 and k are constants. Under this model, isli&gt;m...
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This question is a MATH 102 Calculus for Students in the Social and Biological Sciences

1. A population is said to grow exponentially if its size at time t is given by P(t) = Poe“, Where P0 and k are constants. Under this model, isli&gt;m P(t) = 00. Frequently, a population will actually level off after time. The logistic function is a
model for population growth that takes this into account:
mPO P t = —.
( ) P0 ‘1' (m — P0)6_kmt
Let P(t) be number of internet users in Canada 15 years after 1990 (so 15 = 0 when the
year is 1990, and t = 10 when the year is 2000). There were approximately 0.1 million internet users in Canada in 1990. (a) Find a formula for P(t), assuming that the number of internet users (measured in
millions) in Canada can be approximated by a logistic function with k = 0.0167
and m = 34. (b) Calculate tlim P(t), where P(t) is your logistic function. What does your answer
—)00
mean7 in terms of future internet use in Canada? (c) According to The World Bank, approximately 15.77 million Canadians were in-
ternet users in 2000 (when t = 10). Find a formula for P(t), assuming that this
population is actually growing exponentially. (d) You now have two different models for the number of internet users in Canada.
Use WolframAlpha.com, or other calculation tool to estimate the current number
of internet users in Canada (t = 30). Which model is closest to accurate? (e) You now have two different models for the number of internet users in Canada.
For each of them, use derivative rules to ﬁnd the instantaneous rate of change at
t = 30 (although you should calculate the derivatives by hand, showing each step7
you are welcome to use WolframAlpha.com or other calculation tool to evaluate
each of them at t = 30). Which model predicts greater growth in the population
of Canadian internet users in 2020?

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