The table below represents the displacement of a horse from its barn as a function of time:

Time (hours) x.

0

1

2

3

4

Displacement from barn (feet) y

8

58

108

158

208

part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?

Question

Mathematics

Izabella Dean

24 February, 23:34

The table below represents the displacement of a horse from its barn as a function of time:

Time (hours) x.

0

1

2

3

4

Displacement from barn (feet) y

8

58

108

158

208

part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?

+2

Answers (1)

Know the Answer?

Frances Haas · Answer 1

A. The y-intercept of the function is equal to the value of y when x = 0, so y = 8 ft

This means that the horse is already 8 ft away from the barn initially.

B. The average rate of change represents the slope of the equation. This can be calculated using the formula:

m = (158 - 58) / (3 - 1) = 50 ft / hour

C. Since we already have our y-intercept and slope, we can establish the line equation:

y = 50 x + 8

When y = 508 then x is,

508 = 50 x + 8

50 x = 500

x = 10 hours

It takes 10 hours to reach a displacement of 508 ft.