When an initial amount of money, $\displaystyle {A},$ in dollars, is invested into an account that earns interest continuously, the Future Value of the account after $\displaystyle {t}$ years is given by the formula: $\displaystyle {F}{\left({t}\right)}={A}{e}^{{{r}{t}}},$ where $\displaystyle {r}$ is the annual interest rate earned by the account. Let $\displaystyle {A}=\${13},{000}$ and $\displaystyle {r}={9.9}\%$.

A) What is the value of the account, in dollars, after 13 years? Give your answer rounded to two decimal places.

Answer $

B) What is the exact instantaneous rate of change of the value of the account at exactly 20 years? Give your answer rounded to two decimal places.

Answer: dollars per year

C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $16,883.11 per year? If necessary, round your answer to two decimal places.

Answer: After years.

D) What is the average rate of change of the future value of the account between year 13 and year 17? (Round to the nearest penny/cent.)

Answer: dollars per year. (Round to two decimal places.)