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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.2, Problem 14E

(a)

To determine

**To express:** The distance in terms of the time elapsed.

Expert Solution

The distance *d* in terms of time elapsed is,

Let *d* be the distance traveled in miles and the *t* be the time elapsed in hours.

When *t* = 0, the distance is 0 which can be expressed as (0, 0).

Since he passes the Ann Arbor at 50 minutes, *t* = 50 minutes or

The distance traveled is 40 miles. That is, at

Use the obtained two points and find the slope *m* as follows.

Thus, the slope

Use the slope
*d* in terms of time elapsed *t* as follows.

Thus, the required function is

(b)

To determine

**To sketch:** The graph of the distance equation obtained in part (a).

Expert Solution

Let *x*-axis be represented the time in hours and the *y*-axis be represented the distance in miles.

Given that the distance function of elapsed time is

Obtain the value of *d* for various values of *t* and draw the graph of *d* as shown below in Figure 1.

From Figure 1, it is observed that function is a linear function.

(c)

To determine

**To find:** The slope of the graph drawn in part (b); explain the meaning of slope.

Expert Solution

The slope is 48, which represents the rate of change of the distance in miles.

The equation
*m* is slope and *c* is the *y*-intercept.

Thus, the slope of the Figure 1 shown in part (b) is 48. It represents that the rate of change of the distance in miles.

Moreover, it is observed that there is a decrease in the distance when time increases and hence it is in direct variation. The distance covered in an hour is 48 miles.