Posted by **kayla** on Friday, November 21, 2008 at 3:09pm.

the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now?

the equation for the exponential equation is: A=ao e ^ -kt

ao is the original amount

a is what the population will be

t is the amount of time

k is the rate of growth

- math -
**Reiny**, Friday, November 21, 2008 at 3:27pm
I don't see why the exponent is negative since this an exponentional growth, the negative usually indicates decay.

Anyway...

I would use A = a (e^kt), where t is months

using << the population doubled in size over an 18 month period >>

2 = 1(e^18k)

ln 2 = 18k

k = ln 2/18

so A = 1000 (e^(24*ln2/18))

= 1000(2.51984)

= 2520

another way would be to use

A = 1000(2)t/k and put in t=24

A = 1000(2^1.3333333)

= 2520

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