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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.2, Problem 18E

(a)

To determine

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

Expert Solution

The equation of the monthly cost in terms of the distance driven *d* is

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 *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

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.

Thus, the slope is

Use the slope *C* in terms of *d* as follows.

Thus, the required equation is

(b)

To determine

**To predict:** The monthly cost of driving 1500 miles.

Expert Solution

The monthly cost of driving 1500 miles is $635.

From part (a), the equation of the monthly cost in terms of the distance driven *d* is

Substitute

Thus, the cost of driving 500 miles is $635.

(c)

To determine

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

Expert Solution

Let *x*-axis represents the number of miles driven and *y*-axis represents the monthly cost in dollars.

From part (a), the equation of the monthly cost as a function of distance driven is

Obtain the values of *C* for several values of *d* as tabulated in Table 1 and draw the graph as shown below in Figure 1.

d | C |

0 | 260 |

500 | 385 |

1000 | 510 |

Table 1

From Figure 1, it is observed that the graph is a straight line as the function is linear.

Also, notice that the cost increases as the number of miles increases. That is, if the distance driven increases by 320, then the cost increases by $80 ($0.25 per mile.)

Thus, the slope is,

(d)

To determine

**To explain:** The meaning of *C*-intercept.

Expert Solution

The *C*-intercept of the cost function is 260 and it represents the fixed manufacturing cost per day.

From part (a), the equation of the monthly cost as a function of the distance driven is

Since it follows a linear function, the constant term *c* is considered as the *y*-intercept.

Thus, the *y*-intercept is 260.

The *C*-intercept represents the fixed monthly cost as it is the constant term.

(e)

To determine

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

Expert Solution

Since the monthly cost is fixed and the cost increases as the distance driven increases, the function follows the linear function.

Thus, the linear function is suitable for this situation.