Question

you're given the population and the growth rate as of 2001 for a country. assume that the growth rate remains the same from year to year. Use an exponential function to model population growth and determine the size of the population in a specific year. population = 1,015 milliongrowth rate = 1.4%year = 2008. the size of the population in 2008 will be about ______ million (round to the nearest hundredth as needed)

Answer 1

1118.7 million

Explanation:

An exponential function has the following form:

`f(x)=A\cdot b^x`

In this case, A is the initial population, b is the growth rate and x is the elapsed time, therefore it would be as follows:

`\begin{gathered} f(x)=1015\cdot(1+0.014)^x \\ f(x)=1015(1.014)^x \end{gathered}`

7 years have passed from 2001 to 2008, we replace to calculate the population in 2008, like this:

`\begin{gathered} f(7)=1015(1.014)^7 \\ f(7)=1118.7 \end{gathered}`

Therefore, the size of the population in 2008 will be about 1118.7 million