Question

If the world's population is growing at the rate of 1.1% per year. Approximately how long will it take for it to double? (ln 2 = 0.69)

• A. 25 years
• B. 97 years
• C. 63 years
• D. 127 years

Answer 1

The correct option is C 63 years

$\mathrm{The}\mathrm{population}\mathrm{growth}\mathrm{follows}\mathrm{the}\mathrm{equation}:P\left(t\right)=P_0{e}^{\mathrm{kt}}\mathrm{We}\mathrm{want}\mathrm{the}\mathrm{population}\mathrm{to}\mathrm{become}\mathrm{twice}\mathrm{the}\mathrm{present}\mathrm{population}.\mathrm{So},P\left(t\right)=2\times P_0\mathrm{Substituting}\mathrm{in}\mathrm{equation}2P_0=P_0{e}^{\mathrm{kt}}2=e^{\mathrm{kt}}(k=1.1\%\mathrm{per}\mathrm{year})\ln 2=\frac{1.1}{100}tt=\frac{\ln 2}{1.1}\times 100=63.01\mathrm{years}$