BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.2, Problem 14E

(a)

To determine

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

Expert Solution

Answer to Problem 14E

The distance d in terms of time elapsed is, d=48t .

Explanation of Solution

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 t=56hrs.

The distance traveled is 40 miles. That is, at t=56hrs. , d=40 which can be expressed as (56,40) .

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

m=400560=40×65=48

Thus, the slope m=48 .

Use the slope m=48 and the point (0, 0) and obtain the equation of distance d in terms of time elapsed t as follows.

yy1=m(tx1)d0=48(t0)d=48t

Thus, the required function is d=48t .

(b)

To determine

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

Expert Solution

Explanation of 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 d=40t .

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

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.2, Problem 14E

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

Answer to Problem 14E

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

Explanation of Solution

The equation d=40t is in the form of y=mx+c in which 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.

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