Question

Find the average rate of change of the given function over the interval 4 < a < 7.

A) 4
B) 5
C) 6
D) 8

Answer 1

The average rate of change of the given function over the interval 4 < a < 7 is 3.

Step-by-step explanation:

To find the average rate of change of the given function over the interval 4 < a < 7, we need to find the slope of the line connecting the two points on the graph of the function corresponding to a = 4 and a = 7.

First, let's find the corresponding values of P for a = 4 and a = 7 using the equation P = 3Q - 8:

For a = 4, P = 3(4) - 8 = 12 - 8 = 4

For a = 7, P = 3(7) - 8 = 21 - 8 = 13

Next, we'll use the slope formula: Average rate of change = (Change in P) / (Change in a)

Change in P = 13 - 4 = 9

Change in a = 7 - 4 = 3

Average rate of change = (9) / (3) = 3