When the annual rate of inflation averages 4% over the next 10 years, the approximate cost...

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When the annual rate of inflation averages 4% over the next 10 years, the approximate cost C of goods or services during any year in that decade is given below, where t is the time in years and P is the present cost. C(t) = P(1.04) (a) Suppose the price of an oil change for your car is presently $23.78. Estimate the price (in dollars) 10 years from now. (Round your answer to the nearest cent.) C(10) $35.20 = (b) Find the rates of change of C with respect to t when t = 1 and t = 9. (Round your coefficients to three decimal places.) at t = 1 att = 9 X X 0 (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 4% over the next 10 years, the approximate cost C of goods or services during any year in that decade is given below, where t is the time in years and P is the present cost. C(t) = P(1.04) (a) Suppose the price of an oil change for your car is presently $23.78. Estimate the price (in dollars) 10 years from now. (Round your answer to the nearest cent.) C(10) $35.20 = (b) Find the rates of change of C with respect to t when t = 1 and t = 9. (Round your coefficients to three decimal places.) at t = 1 att = 9 X X 0 (c) Verify that the rate of change of C is proportional to C. What is the constant of proportionality?