Chapter 4.6, Problem 19PE

The populations of two countries are given for January 1, 2000, and for January 1, 2010.

a. Write a function of the form $P\left(t\right)=P_0{e}^{kt}$ to model each population $P\left(t\right)$ (in millions) t years after January 1, 2000. (See Example 3 )

Country	Population in 2000 (millions)	Population in 2010 (millions)	$P\left(t\right)=P_0{e}^{kt}$
Australia	19.0	22.6
Taiwan	22.9	23.7

b. Use the model, from pan (a) to approximate the population on January 1, 2020, for each country. Round to the nearest hundred thousand.

c. 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?

d. Use the models from pan (a) to predict the year during which each population would reach 30 million if this trend continues.