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The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 1.6% per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2017. Round your answer to 1 decimal place.

Sagot :

The form of an exponential growth model is:

[tex]y=y_0e^{rt}[/tex]

Where:

• y0 is the initial population

,

• r is the rate of annual growth, in decimal

,

• t are years since 1987

In this case:

y0 is 5 billion.

The annual growth rate is 1.6%. To covert to decimal, we divide by 100:

[tex]\frac{1.6}{100}=0.016[/tex]

r = 0.016

And t are the years since 1987. We want to find the population in 2017. Then:

[tex]t=2017-1987=30[/tex]

We can construct the model equation:

[tex]y=5,000,000,000e^{0.016\cdot30}[/tex]

And solve:

[tex]y=8,080,372,011[/tex]

This is the projected world population in 2017

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