A driver has to pay an annual road tax of $150. His car does 50 kilometers to one gallon which costs 50 cents per gallon. The car is serviced every 5000 kilometers at a cost of $40, and depreciation is calculated in cents by multiplying the square of the mileage by 0.01. (I) If he covers x kilometers in a year, compute an expression for the total cost in traveling x kilometers and the average total cost per kilometer. (ii) Show that the annual mileage which will minimize the average total cost per kilometer is around 1049 miles.

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 driver has to pay an annual road tax of $150. His car does 50 kilometers to one gallon which costs 50 cents per gallon. The car is serviced every 5000 kilometers at a cost of $40, and depreciation is calculated in cents by multiplying the square of the mileage by 0.01.

(I) If he covers x kilometers in a year, compute an expression for the total cost in traveling x kilometers and the average total cost per kilometer.

(ii) Show that the annual mileage which will minimize the average total cost per kilometer is around 1049 miles.

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