Question

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?

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.