Question

If a population grows 10 % each year, what is the annual continuous growth rate?

Answer 1

I believe it's 365(.10) but I'm not 100% sure

Answer 2

If the population grows 10% each year, then the population P after n years is:
\(\large P = P_0(1.1)^n\) ----- (1)

If the population has a continuous growth rate of 'r', then the population P after n years is: \(\large P = P_0(e)^{rn} = P_0(e^r)^n\) ----- (2)

Comparing (1) and (2): \(\large e^r = 1.1 \). Take natural logarithm on both sides:
\(\large r = \ln(1.1) = 0.0953\)

Multiply by 100 to convert decimal to percentage:
Continuous growth rate = \(\large 0.0953 \times 100 = 9.53\%\)