Answer:
17.3 years
Explanation:
For an investment compounded continuously, the amount, A(t) in the account after a period of t is given by:
[tex]A(t)=A_oe^{rt}[/tex]• When the initial amount, Ao is doubled, A(t)=2Ao
,• Interest Rate = 4% =0.04
Substitute these values into the equation:
[tex]2A_0=A_oe^{0.04t}[/tex]We solve the equation for t:
[tex]\begin{gathered} \text{Divide both sides by }A_0 \\ \frac{2A_0}{A_o}=\frac{A_oe^{0.04t}}{A_o} \\ e^{0.04t}=2 \\ \text{Take the natural log \lparen ln\rparen of both sides} \\ ln(e^{0.04t})=\ln(2) \\ 0.04t=\ln(2) \\ \text{ Divide both sides by 0.04} \\ t=\frac{\ln(2)}{0.04} \\ t=17.3\text{ years} \end{gathered}[/tex]The doubling time is 17.3 years (rounded to the nearest tenth).