Find the average rate of change of the function g(x)= 1/4 ×2^x over the interval 3 less than or equal to x less than or equal to 7.
To find the average rate of change of the function g(x) = (1/4) * 2^x over the interval 3 ≤ x ≤ 7, we need to calculate the difference in the function values at the two endpoints (7 and 3) and divide it by the difference in the x-values:
g(7) = (1/4) * 2^7 = (1/4) * 128 = 32
g(3) = (1/4) * 2^3 = (1/4) * 8 = 2
The difference in the function values is 32 - 2 = 30.
The difference in the x-values is 7 - 3 = 4.
Therefore, the average rate of change of g(x) over the interval 3 ≤ x ≤ 7 is 30/4 = 7.5.