Find the average rate of change of the function g left-parenthesis x right-parenthesis equals one-fourth times 2 superscript x baseline over the interval 3 less-than-or-equal-to x less-than-or-equal-to 7.
(1 point)
Responses
7.5
7.5
10
10
15
15
30
To find the average rate of change of a function over a given interval, we need to find the change in the function's values divided by the change in the interval.
In this case, the function is g(x) = 1/4 * 2^x and the interval is from 3 to 7.
To find the change in the function's values, we need to subtract the function's value at the beginning of the interval from its value at the end of the interval.
g(7) = 1/4 * 2^7 = 1/4 * 128 = 32
g(3) = 1/4 * 2^3 = 1/4 * 8 = 2
Change in the function's values = g(7) - g(3) = 32 - 2 = 30
The change in the interval is 7 - 3 = 4.
Average rate of change = Change in the function's values / Change in the interval = 30 / 4 = 7.5.
Therefore, the average rate of change of the function g(x) over the interval 3 ≤ x ≤ 7 is 7.5.