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The table below represents the displacement of a turtle from its nest as a function of time:


Time (hour) | Displacement from nest (miles
x | y
0 | 5
1 | 27
2 | 49
3 | 71
4 | 93

Part A: What is the y-intercept of the function, and what does this tell you about the turtle? (4 points)

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points)

Part C: What would be the domain of the function if the turtle continued to walk at this rate until it traveled 225 miles from the nest? (2 points)

Respuesta :

nobillionaireNobley
The y-intercept is the value of y when x = 0, here, y-intercept = 5.
It is the initial position of the turtle.

Average rate of change = y(4) - y(1) / 4 - 1 = 93 - 27 / 3 = 66/3 = 22
It represents the displacement per hour from the first hour to the fourth hour.

If it travelled at 22 miles per hour till it has travelled 225 miles, it must have travelled 225/22 = 10.2 hours.
Domain is 0 ≤ t ≤ 10.2

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