When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of goods or services during any year in that decade is C(t) = P(1.05)t where t is the time in years and P is the present cost. (a) The price of an oil change for your car is presently $24.95. Estimate the price 10 years from now. (b) Find the rates of change of C with respect to t when t = 1 and t = 8. (c) Verify that the rate of change of C is proportional to C. What is the constant of proportionality?
When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of goods or services during any year in that decade is C(t) = P(1.05)t where t is the time in years and P is the present cost. (a) The price of an oil change for your car is presently $24.95. Estimate the price 10 years from now. (b) Find the rates of change of C with respect to t when t = 1 and t = 8. (c) Verify that the rate of change of C is proportional to C. What is the constant of proportionality?
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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When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of goods or services during any year in that decade is C(t) = P(1.05)t where t is the time in years and P is the present cost. (a) The price of an oil change for your car is presently $24.95. Estimate the price 10 years from now. (b) Find the rates of change of C with respect to t when t = 1 and t = 8. (c) Verify that the rate of change of C is proportional to C. What is the constant of proportionality?
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