The average rate of change between the interval x = 0.5 to x = 3.5 is: 5.
x = 3.5 represents 3.5 hours after noon.
How to Find Average Rate of Change Over an Interval
Given an interval of x = a to x = b, the average rate of change over the given interval of a function can be calculated using the formula below:
[tex]\frac{f(b) - f(a)}{b - a}[/tex]
Given table representing the function as shown in the image attached below, let's determine the average rate of change for x = 0.5 to x = 3.5.
a = 0.5
f(a) = 47 (from the table, when x = 0.5, y = 47)
b = 3.5
f(b) = 62 (from the table, when x = 3.5, y = 62)
Plug the values into [tex]\frac{f(b) - f(a)}{b - a}[/tex]
Average rate of change = [tex]\frac{62 - 47}{3.5 - 0.5} = \frac{15}{3} = 5[/tex]
Average rate of change = 5
x = 3.5 represents 3.5 hours after noon.
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