Posted by **Chris** on Wednesday, February 18, 2009 at 12:02am.

The population of a city is p=2500 e^(kt) where t = 0 represents the year 2000. in 1945 the population was 1350. Find the value of k and use this result to predict the population in the year 2010.

- algebra 2/trig -
**Reiny**, Wednesday, February 18, 2009 at 12:14am
if the year 2000 matches t = 0, then

the year 1945 matches t = -55

so we have 1350 = 2500e^(-55k)

.54 = e^(-55k)

using natural logs,

-55k = ln(.54)

k = .011203384

so the equation is p = 2500e^(.011203384t)

in 2010 , t = 10

so

p = 2500E(.011203384*10)

= 2796

- algebra 2/trig -
**Chris**, Wednesday, February 18, 2009 at 12:21am
You are a god.

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