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## Homework Statement

In 2000 the population of a country was estimated to be 8.23 million. In 2010 the population was 9.77 million.

Assume that the number of people P(t) in millions at time t (in years since 2000) is modeled by the exponential growth function.

P(t) = Ae

^{kt}

Find P(t) giving the two constants in it to 2 significant figures.

## Homework Equations

P(t) = Ae

^{kt}

## The Attempt at a Solution

P(0) = 8.23x10

^{6}so Ae

^{0k}= 8.23x10

^{6}

P(10) = 9.77x10

^{6}so Ae

^{10k}= 9.77x10

^{6}

Divide to eliminate A:

Ae

^{0k}= 8.23x10

^{6}/ Ae

^{10k}= 9.77x10

^{6}= e

^{0k-10k}= 8.23x10

^{6}/ 9.77x10

^{6}= e

^{-10 k}= 8.23x10

^{6}/ 9.77x10

^{6}

(I am not certain that this step is right)

-10k = ln 8.23x10

^{6}/ 9.77x10

^{6}

k = 0.01917945693

To find A:

Ae

^{10k}= 9.77x10

^{6}

Ae

^{10*0.01917945693}= 9.77x10

^{6}

A = 9.77x10

^{6}/ e

^{10*0.01917945693}= 8064904.714

These values for k and A seem to produce 9.77x10

^{6}when 10 (years) is plugged into the function, however I can't seem to produce 8.23x10

^{6}at 0 years since 2000 and I can't seem to see why, any help would be much appreciated!