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Suppose 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: 0/ 2 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 I %. The populations of two countries are given for January 1, 2000, and for January 1, 2010. Part: 0 / 3 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 e (millions) (millions) Australia 19.0 22.6 P (1) = 1 X 5 Taiwan 22.9 23.7 P (t) =Refer to the model Q (t) =Q0670'000121t used for radiocarbon dating. At an archeological site, scientists uncovered human remains. A sample from a human bone taken from the site showed that 28.7% of the carbon14 still remained. How old is the sample? Round to the nearest year. Do not round intermediate calculations. The sample from the human remains is approximately' I years old. The population of the Canada P (t) (in millions) since January 1, 1900, can be approximated by 55.4 P(t) = -0.0252t , where t is the number of years since January 1, 1900. 1+9.8e Canadian Population by Year 60 y = P(t) Population (millions) 0 50 100 150 200 250 300 Year (t = 0 represents 1900) Part: 0 / 6 Part 1 of 6 (a) Evaluate P(0) (round to the nearest tenth of a million) and interpret its meaning in the context of this problem. The Canadian population was approximately million on January 1, (Choose one) X 5 1900 1910 1920