Given,
A population doubles every 27 years.
a. Let initial population be 1 and after 27 years it becomes 2.
Considering r as the rate of annuall growth we have,
[tex]\begin{gathered} 1(1+r)^{27}=2 \\ \Rightarrow27\ln (1+r)=\ln 2 \\ \Rightarrow\ln (1+r_{})=\frac{0.693}{27} \\ \Rightarrow1+r=1.0257 \\ \Rightarrow r=0.026 \end{gathered}[/tex]Thus annual growth rate is 2.6%
b. For continuous growth,
[tex]\begin{gathered} 1(e^{27x})=2 \\ \Rightarrow27x=0.693 \\ \Rightarrow x=0.025 \end{gathered}[/tex]The continuous growth rate is _2.5___% per year
