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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 = $9,000 and r = 9.3%. A) What is the value of the account, in dollars, after 12 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 19 years? Give your answer rounded to two decimal places. dollars per year Answer: C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $16,412.92 per year? If necessary, round your answer to two decimal places. Answer: After years.

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 = $9,000 and r = 9.3%. A) What is the value of the account, in dollars, after 12 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 19 years? Give your answer rounded to two decimal places. dollars per year Answer: C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $16,412.92 per year? If necessary, round your answer to two decimal places. Answer: After years.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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: \( F(t) = Ae^{rt} \), where \( r \) is the annual interest rate earned by the account. Let \( A = \$9,000 \) and \( r = 9.3\% \). **A) What is the value of the account, in dollars, after 12 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 19 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 $16,412.92 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 12 and year 15 (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.)
Transcribed Image Text: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: \( F(t) = Ae^{rt} \), where \( r \) is the annual interest rate earned by the account. Let \( A = \$9,000 \) and \( r = 9.3\% \). **A) What is the value of the account, in dollars, after 12 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 19 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 $16,412.92 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 12 and year 15 (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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