Population Growth

**magentarita** · August 14th 2008, 02:49 AM

The population of a midwestern city follows the exponential law. If the population decreased from 900,000 to 800,000 from 1993 to 1995, what will the population be in 1997?

Extra: What is the population in 2008?

**mr fantastic** · August 14th 2008, 03:06 AM

Originally Posted by magentarita

The population of a midwestern city follows the exponential law. If the population decreased from 900,000 to 800,000 from 1993 to 1995, what will the population be in 1997?

Extra: What is the population in 2008?

$P = P_0 e^{kt}$ where t is number of years measured from start of 1993.

At t = 0, P = 900,000 therefore $P_0 = 900,000$ and so $P = 900,000 e^{kt}$ .

Substitute t = 2, P = 800,000 and solve for k:

$800,000 = 900,000 e^{2k} \Rightarrow \frac{8}{9} = e^{2k} \Rightarrow \ln \frac{8}{9} = 2k \Rightarrow k =$ .... (I'd suggest getting an answer correct to five decimal places).

Now substitute the values of t corresponding to 1997 and 2008 and solve for P in each case.

**magentarita** · August 14th 2008, 12:38 PM

I will play with this question to find k.

Thanks

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