Final answer:
The correct answer is option c. To find the average rate of change over the interval [2, 5] for the function g(x) = log₂(x + 3) 4, we calculate the difference in the function values at x = 5 and x = 2, and divide it by the difference in the x-values. The answer is 7/3.
Step-by-step explanation:
To find the average rate of change over the interval [2, 5], we need to calculate the difference in the function values at x = 5 and x = 2, and divide it by the difference in the x-values. The function given is g(x) = log₂(x + 3) + 4. So, g(5) = log₂(5 + 3) + 4 = log₂(8) + 4 = 3 + 4 = 7, and g(2) = log₂(2 + 3) + 4 = log₂(5) + 4.
Therefore, the average rate of change is (7 - (log₂(5) + 4))/(5 - 2). Simplifying further, we get (7 - log₂(5) - 4)/3, which is the same as (3 - log₂(5))/3. Therefore, the answer is option c. 7/3.