When an initial amount of money, A,A, in dollars, is invested into an account that earns interest continuously, the Future Value of the account after tt years is given by the formula: F(t)=Aert,F(t)=Aert, where rr is the annual interest rate earned by the account. Let A=$24,000A=$24,000 and r=7.9%r=7.9%.
A) What is the value of the account, in dollars, after 30 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 9 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 $37,412.18 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 30 and year 33 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.)
Answer: dollars per year. (Round to two decimal places.)