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A lump sum of $1000 is invested at 4.5% compounded continuously. (a) Write the function for the model that gives the future value of the investment in dollars after t years. F(t) dollars (b) Write a model for the rate of change of the value of the investment. (Hint: Let b = e0.045 and use the rule for f(x) = b*.) dollars per year F'(t) = (c) How much is the investment worth after 8 years? (Round your answer to two decimal places.) $ (d) How quickly is the investment growing after 8 years? (Round your answer to three decimal places.) $ per year

A lump sum of $1000 is invested at 4.5% compounded continuously. (a) Write the function for the model that gives the future value of the investment in dollars after t years. F(t) dollars (b) Write a model for the rate of change of the value of the investment. (Hint: Let b = e0.045 and use the rule for f(x) = b*.) dollars per year F'(t) = (c) How much is the investment worth after 8 years? (Round your answer to two decimal places.) $ (d) How quickly is the investment growing after 8 years? (Round your answer to three decimal places.) $ per year

Calculus: Early Transcendentals
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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A lump sum of $1000 is invested at 4.5% compounded continuously. (a) Write the function for the model that gives the future value of the investment in dollars after t years. F(t) dollars (b) Write a model for the rate of change of the value of the investment. (Hint: Let b = e0.045 and use the rule for f(x) = b*.) dollars per year F'(t) = (c) How much is the investment worth after 8 years? (Round your answer to two decimal places.) $ (d) How quickly is the investment growing after 8 years? (Round your answer to three decimal places.) $ per year
Transcribed Image Text:A lump sum of $1000 is invested at 4.5% compounded continuously. (a) Write the function for the model that gives the future value of the investment in dollars after t years. F(t) dollars (b) Write a model for the rate of change of the value of the investment. (Hint: Let b = e0.045 and use the rule for f(x) = b*.) dollars per year F'(t) = (c) How much is the investment worth after 8 years? (Round your answer to two decimal places.) $ (d) How quickly is the investment growing after 8 years? (Round your answer to three decimal places.) $ per year
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