Chapter 6.5, Problem 43E

(a)

To determine

The expression for the average value of the money in the account during the $3$- year time period, that is $0\le t\le 3$, when the amount in the savings account at the end of $t$ years is $1000e{}^{rt}$.

(b)

To determine

The rate of interest $r$ for the function of the average amount, $\frac{1000}{3r}\left(e^{3r}-1\right)$ if the average amount in the account is $\$1070.60$ during the $3$-year period.