Question

The function H is continuous and passes through the points (7,3 1 k + )

and (−2 1, 4 k k + ). If the average rate of change on H on the interval
[7, 2 1 − k + ] is equal to 0.25, what is the value of k ?

Answer 1

To find the value of k, we can use the average rate of change formula. The average rate of change on the interval [7, 21 - k] is equal to the difference in the y-values divided by the difference in the x-values. Solving for k gives k = 0.25.

Step-by-step explanation:

To find the value of k, we can use the average rate of change formula. The average rate of change on the interval [7, 21 - k] is equal to the difference in the y-values divided by the difference in the x-values. Using the given points, we have:

Average rate of change = (4k - (3+1k)) / (-2 - 7) = 0.25

Now we can solve for k:

4k - 3 - k = 0.25(-2 - 7)

3k - 3 = -2.25

3k = -2.25 + 3

3k = 0.75

k = 0.75/3

k = 0.25