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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 5\le x \le 75≤x≤7.

Sagot :

MrRoyalidn

Answer:

[tex]Average\ Rate = 48[/tex]

Step-by-step explanation:

Given

See attachment for table

Required

Determine the average rate of change over [tex]5\le x \le 7[/tex]

Average rate of change is calculated using:

[tex]Average\ Rate = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex]a \le x\le b[/tex]

In this case:

[tex]a = 5;\ \ \ b = 7[/tex]

[tex]Average\ Rate = \frac{f(b) - f(a)}{b - a}[/tex]

[tex]Average\ Rate = \frac{f(7) - f(5)}{7 - 5}[/tex]

[tex]Average\ Rate = \frac{f(7) - f(5)}{2}[/tex]

From the table:

[tex]f(7) = 108[/tex]

[tex]f(5) = 12[/tex]

The expression becomes

[tex]Average\ Rate = \frac{108 - 12}{2}[/tex]

[tex]Average\ Rate = \frac{96}{2}[/tex]

[tex]Average\ Rate = 48[/tex]

View image MrRoyal
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