Question

a population of bobcats increase by 5% per year if the population is currently 40 in how many years will the population reach 80 round your answer to the nearest tenth. The population will reach 80 in about _____years​

Answer 1

$\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t$