   Chapter 1.2, Problem 20E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### 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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