Question

it is predicted that the population of a particular state will double every 25 years.
a) determine the annual and monthly growth rate. express your answer as percents.

b)determine the continuous growth rate per year. Express your answer as a percent.

Answer 1

\[P(y) = P(0) 2^{\frac{y}{25}}\]
If we let y = 1 then P(1) = (1.02811...) P(0), that is, P(1) is 2.8% more than P(0), so that's the growth rate for 1 year. If we let y = 1/12 (one month) then P(1/12) = (1.00231...)P(0), that is, P(1/12) is 0.23% more than P(0), so that is the growth rate for 1 month.

I'm not sure what you mean by a "continuous" growth rate, but perhaps you mean re-expressing this as an exponential:
\[P(y) = P(0) (e^{\ln 2})^{\frac{y}{25}} = P(0) e^{\frac{\ln 2}{25} y}\]
Here the continuous growth rate would be (ln 2)/25 = 0.027726... or 2.8%.

Answer 2

yeah i dont undertant part B either but i think your right, thank you so much