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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)

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ANSWER:

1118.7 million

STEP-BY-STEP EXPLANATION:

An exponential function has the following form:

[tex]f(x)=A\cdot b^x[/tex]

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:

[tex]\begin{gathered} f(x)=1015\cdot(1+0.014)^x \\ f(x)=1015(1.014)^x \end{gathered}[/tex]

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

[tex]\begin{gathered} f(7)=1015(1.014)^7 \\ f(7)=1118.7 \end{gathered}[/tex]

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

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