Population Growth

**AlgebraicallyChallenged** · May 14th 2009, 04:08 PM

Dear Forum I am having problems with the following any feedback would be appreciated:
If the population in a particular country is growing at 1.7% compounded continuously, how long will it take the population to double? (Round up to the next higher year if not exact.)

thanks -AC-

**pickslides** · May 14th 2009, 07:31 PM

Try

$P=P_0e^{rt}$

where $P_0 =$ initial population, r = growth rate and t = time in years and P= $2\times P_0$

you should find

$2P_0=P_0e^{1.07t}$

$2=e^{1.07t}$

$ln(2)=1.07t$

$t= \frac{ln(2)}{1.07}$ years

**TKHunny** · May 14th 2009, 08:35 PM

Something fishy going on there. ln(2)/1.07 < 1. It's growing at 1.7% per year and doubles in less than a year?

Using the classical Rules of 72, we get an approximation of 72 / 1.7 = 42.353 years. Let's find a model that produces a result in this neighborhood.

$2 = 1.017^{t}$

Or, if you insist on e-base.

$2 = e^{ln(1.017)*t} = e^{0.01685712*t}$

**dwat** · May 19th 2009, 04:30 AM

Originally Posted by pickslides

Try

$P=P_0e^{rt}$

where $P_0 =$ initial population, r = growth rate and t = time in years and P= $2\times P_0$

you should find

$2P_0=P_0e^{1.07t}$

$2=e^{1.07t}$

$ln(2)=1.07t$

$t= \frac{ln(2)}{1.07}$ years

why is it that you've used ${1.07}$ ??

Shouldnt r be $1.017$ ?? Or was just a human error? because if $ln {2} / 1.07 < 1$ than that will be a decay not growth wouldn't it?

**pickslides** · May 19th 2009, 02:01 PM

correct, I did use the wrong value.

I hope displaying the methodology helped all the same...

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