Question

Using the function g(x) = log₂(x-5) + 1, find the average rate of change of g on the interval [6,13].

a) 1/7

b) 2/7

c) 1/3

d) 2/3

Answer 1

The average rate of change of the function g(x) on the interval [6,13] is 3/7. This result is obtained by calculating the change in function values at x = 6 and x = 13 and dividing by the interval length. None of the given options match this correct answer.

Step-by-step explanation:

To find the average rate of change of the function g(x) = log₂(x-5) + 1 on the interval [6,13], we need to calculate the difference in the function's values at the endpoints of the interval and then divide by the length of the interval.

First, calculate g(6) and g(13):
g(6) = log₂(6-5) + 1 = log₂(1) + 1 = 0 + 1 = 1
g(13) = log₂(13-5) + 1 = log₂(8) + 1 = 3 + 1 = 4

Now, find the average rate of change:
Average rate of change = (g(13) - g(6)) / (13 - 6) = (4 - 1) / (7) = 3 / 7

Among the given options, none matches the correct calculation of 3 / 7. Hence, the correct answer is not listed among the options a) 1/7, b) 2/7, c) 1/3, d) 2/3.