Chapter 1.1, Problem 45E

To determine

The type of function that can be used to model the data and then to estimate the speed of car when it is $20$ yards past the intersection.

Answer to Problem 45E

Function belongs to family of absolute value functions and the speed of the car when it is $20$ yards past the intersection is $8miles/hour$ .

Explanation of Solution

Given information: Table containing data values of displacement and speed is given.

Calculation:

The data appears to lie on a V-shaped graph that resembles the graph of an absolute value function, so, data can be modeled with an absolute value function.

  

It can be observed from the graph that when $x=20,y=8$ .

Verifying the observation from the graph,

Speed is increasing after $10yards$ , so displacement per every unit increase in speed is $\frac{50-10}{20-4}=\frac{40}{16}=2.5$

When the displacement was 10, speed was $4$ , when displacement became $20$ speed would be,

  $4+\frac{20-10}{2.5}=4+\frac{10}{2.5}=4+4=8$

So, the speed of the car when it is $20$ yards past the intersection is $8miles/hour$ .

Thus, function belongs to family of absolute value functions and speed of the car when it is $20$ yards past the intersection is $8miles/hour$ .