The populations of two countries are given for January 1, 2000, and for January 1, 2010. Part 1 of 3 (a) Write a function of the form P (t) = Poe" to model each population P (t) (in millions) t years after January 1, 2000. Round the value of k to five decimal places Country Population Population P (t) = Pekt in 2000 in 2010 (millions) (millions) P t = 19e 0.01735 t Australia 19.0 22.6 Taiwan 22.9 23.7 P (t) = 0.00343 t 22.9e Part: 1 / 3 Part 2 of 3 (b) Use the models from part (a) to approximate the population on January 1, 2020, for each country. Round to the nearest hundred thousand. Australia had fewer people than Taiwan in the year 2000, yet from the result of part (b), Australia would have more people in the year 2020? Why? The population of Australia on January 1, 2020, would reach million. X 5 The population of Taiwan on January 1, 2020, would reach million. Australia would have more people than Taiwan in the year 2020 because the (Choose one) is (Choose one) Australia than for Taiwan. growth rate or initial population greate r or lessSuppose that $100,000 from a retirement account is invested in a large cap stock fund. After 30 yr, the value is $176,985.03. Part 1 of2 $ (a) Use the model A=Pert to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps. The average rate is approximately I 1.9 I %. Part: 1/2 Part2on (b) How long will it take the investment to reach onequarter million dollars? Round to the nearest tenth of a year. Round values in intermediate steps to three decimal places. It will take approximately I I years. X S The population of the Canada P (t) (in millions) since January 1, 1900, can be approximated by 55.4 P(t) = 1 +9 8 0.0252t' Where i is the number of years since January 1, 1900. Canadian Population by Year 60 y = P(t) Population (millions) 0 50 100 150 200 250 300 Year (t = 0 represents 1900)Part 2 of 6 (b) Use the function to approximate the Canadian population on January 1, 2040. Round to the nearest tenth of a million. The model approximates that the Canadian population will be approximately million on January 1, 2040. X