A population is said to grow erponentially if its size at time t is given by...

 

Transcribed Image Text:

A population is said to grow erponentially if its size at time t is given by P(t) = Poekt, where Po andk are constants. Under this model, lim P(t) = %3D = 0. 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) Po + (m – Po)e-kmt" Let P(t) be number of internet users in Canada t years after 1990 (so t = 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 lim P(t), where P(t) is your logistic function. What does your answer t00 mean, 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 erponentially. (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 step, 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? A population is said to grow erponentially if its size at time t is given by P(t) = Poekt, where Po andk are constants. Under this model, lim P(t) = %3D = 0. 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) Po + (m – Po)e-kmt" Let P(t) be number of internet users in Canada t years after 1990 (so t = 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 lim P(t), where P(t) is your logistic function. What does your answer t00 mean, 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 erponentially. (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 step, 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?

Answer rating: 100% (QA)

dejiste funcfim PLO mPo kmt P m fo e giuan afoandtin ... View the full answer