Chapter 3.2, Problem 44E

a.

To determine

Whether the given table represents a linear function or not.

Time (hours), t	Distance (miles), d
1	60
3	180
5	310

Answer to Problem 44E

Non linear function

Explanation of Solution

A linear function is a function with constant rate of change. That is as t values are increased or decreased by same amount, the d values also increases or decreases by same amount.

Here t values are all increasing by 2.

And, for $t=1$ , $d=60$ and for $t=3$ , $d=180$

So, the d value increases by,

  $180-60=120$

Also, for $t=3$ , $d=180$ and for $t=5$ , $d=310$

So, the d value increases by,

  $310-180=130$

Thus, the increase in d value is not constant.

Hence, the function represented by table is not linear.

b.

To determine

Whether the claim, “Car B is moving at faster rate than car A” correct or not.

Answer to Problem 44E

Correct

Explanation of Solution

The distance d of car A from rental store after t hours is given by:

  $d=50t$

So, distance travelled by car A in 1 hour is 50 miles.

The distance of car B from rental store after t hours is given by the table:

Time (hours), t	Distance (miles), d
1	60
3	180
5	310

From the given table the distance travelled by car B in 1 hour is 60 miles.

Hence, the claim is correct and Car B is moving at faster rate.