Chapter 4.6, Problem 29PE

A function of the form $P\left(t\right)=a{b}^t$ represents the population (in millions) of the given country t years after January 1, 2000. (See Example 4 )

a. Write an equivalent function using base e; that is, write a function of the form $P\left(t\right)=P_0{e}^{kt}$. Also, determine the population of each country for the year 2000.

Country	$P\left(t\right)=a{b}^t$	$P\left(t\right)=P_0{e}^{kt}$	Population in 2000
Costa Rica	$P\left(t\right)=4.3{\left(1.0135\right)}^t$
Norway	$P\left(t\right)=4.6{\left(1.0062\right)}^t$

b. The population of the two given countries is very close for the year 2000, but their growth rates are different. Use the model to approximate the year during which the population of each country reached 5 million.

c. Costa Rica had fewer people in the year 2000 than Norway. Why would Costa Rica reach a population of 5 million sooner than Norway?