Thread: Population Growth

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-

Try

$\displaystyle P=P_0e^{rt}$

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

you should find

$\displaystyle 2P_0=P_0e^{1.07t}$

$\displaystyle 2=e^{1.07t}$

$\displaystyle ln(2)=1.07t$

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

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.

$\displaystyle 2 = 1.017^{t}$

Or, if you insist on e-base.

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

Originally Posted by pickslides

Try

$\displaystyle P=P_0e^{rt}$

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

you should find

$\displaystyle 2P_0=P_0e^{1.07t}$

$\displaystyle 2=e^{1.07t}$

$\displaystyle ln(2)=1.07t$

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

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

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

correct, I did use the wrong value.

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