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11 December, 16:44

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?

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Answers (1)
  1. 11 December, 16:57
    0
    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.
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