Question

the amount of money in an account with continuously compounded interest is given by the formula A

Answer 1

SOLUTION

Given the question as contained in the image on the question tab;

$A=Pe^{rt}$$\begin{gathered} A=2P \\ r=7.5\text{ \%} \\ t=? \\ \end{gathered}$$\begin{gathered} 2P=Pe^{0.075t} \\ Divide\text{ both sides by P;} \\ 2=e^{0.075t} \\ ln2=ln(e^{0.075t}) \\ ln2=0.075t \\ t=\frac{ln2}{0.075} \\ t=9.2\text{ years} \end{gathered}$

Final answer:

9.2 years.