Question

This table shows values represented by an exponential function.

What is the average rate of change for this function for the interval from x=1 to x=3?

(Yes, I know I am giving a lot of points for this.)

Answer 1

Points are

• (1,3)
• (3,27)

Rate of change means we need to find slope

`\\ \sf\longmapsto (y_2-y_1)/(x_2-x_1)`

`\\ \sf\longmapsto (27-3)/(3-1)`

`\\ \sf\longmapsto (24)/(2)`

`\\ \sf\longmapsto 12`

Answer 2

• 12

Explanation:

Average rate of change from x = 1 to x = 3 is:

• difference of y-values / difference of x-values =
• ('y at x = 3' - 'y at x = 1') / ( 3 - 1) =
• (27 - 3) / 2 =
• 24/2 =
• 12