When an initial amount of money, A, in dollars, is invested into an account that earns interest continuously, the Future Value of the account after t years is given by the formula: F(t) = Ae", where r is the annual interest rate earned by the account. Let A = $19,000 and r = 9.4%. A) What is the value of the account, in dollars, after 9 years? Give your answer rounded to two decimal places. Answer $ 44275.83 B) What is the exact instantaneous rate of change of the value of the account at exactly 13 years? Give your answer rounded to two decimal places. dollars per year C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $53,918.76 per year? If necessary, round your answer to two decimal places. Answer: 6061.63 Answer: After 26.25 years. D) What is the average rate of change of the future value of the account between year 9 and year 11 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.) dollars per year. (Round to two decimal places.) Answer:

When an initial amount of money, A, in dollars, is invested into an account that earns interest continuously, the Future Value of the account after t years is given by the formula: F(t) = Ae", where r is the annual interest rate earned by the account. Let A = $19,000 and r = 9.4%. A) What is the value of the account, in dollars, after 9 years? Give your answer rounded to two decimal places. Answer $ 44275.83 B) What is the exact instantaneous rate of change of the value of the account at exactly 13 years? Give your answer rounded to two decimal places. dollars per year C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $53,918.76 per year? If necessary, round your answer to two decimal places. Answer: 6061.63 Answer: After 26.25 years. D) What is the average rate of change of the future value of the account between year 9 and year 11 (i.e. slope of the secant line connecting the points)? (Round to the nearest penny/cent.) dollars per year. (Round to two decimal places.) Answer:

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

When an initial amount of money, A, in dollars, is invested into an account that earns interest
continuously, the Future Value of the account after t years is given by the formula: F(t) = Aet, where r
is the annual interest rate earned by the account. Let A = $19,000 and r = 9.4%.
A) What is the value of the account, in dollars, after 9 years? Give your answer rounded to two decimal
places.
Answer $ 44275.83
B) What is the exact instantaneous rate of change of the value of the account at exactly 13 years? Give
your answer rounded to two decimal places.
dollars per year
Answer: 6061.63
C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by
$53,918.76 per year? If necessary, round your answer to two decimal places.
Answer: After 26.25
years.
D) What is the average rate of change of the future value of the account between year 9 and year 11 (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.)

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