Question

Can someone help me please I don’t get this

Answer 1

`\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll be using this one}}{log_a a^x = x}\qquad \qquad a^(log_a x)=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140\\ P=\textit{original amount deposited}\dotfill & \$70\\ r=rate\to r\%\to (r)/(100)\\ t=years\dotfill &5 \end{cases}`

`140 = 70e^{(r)/(100)\cdot 5} \implies \cfrac{140}{70}=e^{(r)/(20)}\implies 2=e^{(r)/(20)}\implies \log_e(2)=\log_e\left( e^{(r)/(20)} \right) \\\\\\ \log_e(2)=\cfrac{r}{20}\implies \ln(2)=\cfrac{r}{20}\implies 20\ln(2)=r\implies \boxed{13.86\approx r}`