Question

Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 0 < x < 3.

Answer 1

Answer:  104/3

Note: in decimal form, this fraction converts to roughly 34.67

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Explanation:

Highlight the rows that have x = 0 and x = 3. Cross out or cover the other two rows up.

The two rows that have x = 0 and x = 3 show y = f(x) = 4 and y = 108 respectively.

So we have the two points (0,4) and (3,108). We need to find the slope of the line through these points to find the average rate of change from x = 0 to x = 3.

Turn to the slope formula

m = (y2-y1)/(x2-x1)

m = (108-4)/(3-0)

m = 104/3

We cannot reduce the fraction further.

Using a calculator,

104/3 = 34.67 approximately