Suppose that $\$ 11,000$ is invested in a bond fund and the account grows to $\$ 13,900.36$ in $3 \mathrm{yr}$.
Part: 0 / 2
Part 1 of 2
(a) Use the model $A=P e^{r t}$ to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps.
The average rate of return under continuous compounding is approximately $\square \%$.

Step 1 ：Substitute the given values into the formula for continuous compounding: \(A = Pe^{rt}\), we get \(13,900.36 = 11,000 * e^{3r}\)

Step 2 ：Isolate \(e^{3r}\) by dividing both sides by \(11,000\), we get \(e^{3r} = \frac{13,900.36}{11,000} = 1.263669\)

Step 3 ：Take the natural logarithm (ln) of both sides to solve for \(3r\), we get \(3r = ln(1.263669)\)

Step 4 ：Divide by 3 to solve for \(r\), we get \(r = \frac{ln(1.263669)}{3} = 0.0807\)

Step 5 ：Convert this decimal to a percentage by multiplying by 100, we get \(r = 0.0807 * 100 = 8.07\%\)

Step 6 ：Round to the nearest tenth of a percent, the average rate of return under continuous compounding is approximately \(\boxed{8.1\%}\)