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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi.

(a) Express the monthly cost C as a function of the distance driven d. assuming that a linear relationship gives a suitable model.

(b) Use part (a) to predict the cost of driving 1500 miles per month.

(c) Draw the graph of the linear function. What does the slope represent?

(d) What does the C-intercept represent?

(e) Why does a linear function give a suitable model in this situation?

(a)

To determine

To express: The monthly cost in terms of the distance driven d assuming the function follows a linear function.

Explanation

Let d represents the number of miles driven in a month and C represents the monthly cost in dollars.

Recall the general equation of the linear function y=mx+c where m is the slope and c is the y-intercept.

Since the cost function follows a linear function, the equation of the cost C in terms of the number of miles driven d is in the form of C=md+c.

According to the given data, there are two points such as (480, 380) and (800, 460).

Obtain the slope m by using the two point formula as follows.

m=y2y1x2x1=460380800480=80320=14

Thus, the slope is m=14

(b)

To determine

To predict: The monthly cost of driving 1500 miles.

(c)

To determine

To sketch: The graph of the cost as a function of distance driven and interpret the slope.

(d)

To determine

To explain: The meaning of C-intercept.

(e)

To determine

To explain: Why a linear function is suitable for this model.

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th