Question

How long does it take for a deposit of​ $800 to double at​ 8% compounded​ continuously?

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{\$ 1600}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ t=years \end{cases}`

`1600 = 800e^(0.08\cdot t) \implies \cfrac{1600}{800}=e^(0.08t)\implies 2=e^(0.08t) \\\\\\ \log_e(2)=\log_e(e^(0.08t))\implies \log_e(2)=0.08t\implies \ln(2)=0.08t \\\\\\ \cfrac{\ln(2)}{0.08}=t\implies 8.66\approx t\qquad \textit{about 8 years and 241 days}`