Question

A population doubles every 21 years. Assuming exponential growth find the following:

(a) The annual growth rate

(b) The continuous growth rate per year

Plz help, very many thanks math gods

Answer 1

what's the formula for exponential growth?

Answer 2

\[\Large P=P_0(1+r)^t\]

population, \(P\) is given by this formula , where \(P_0\) is initial \(r\) is the annual growth rate , \(t\) is time in years

Answer 3

since it doubles every 21 years:\[\large 2\cancel{P_0}=\cancel{P_0}(1+r)^{21}\]

Answer 4

\[\ln2=21\ln(1+r)\]

r=\[r\\=e^{\ln2/21}-1\\=2^{1/21}-1\\ \approx3.356\ \%\]