We can conclude that the average rate of change for function f(x) is steeper than the average rate of change for function g(x) over the interval 5 ≤ x ≤ 7.
To compare the average rates of change for the pair of functions f(x) = -0.4x² and g(x) = -0.8x² over the interval 5 ≤ x ≤ 7, we can first calculate the average rate of change for each function separately.
The average rate of change of a function over an interval is defined as the change in the function's output values divided by the change in its input values. In other words, it represents the slope of the secant line that intersects the function's graph at the interval's endpoints.
For function f(x) = -0.4x², the average rate of change over the interval 5 ≤ x ≤ 7 can be calculated as follows:
Average rate of change of f = (f(7) - f(5)) / (7 - 5)
= (-0.4(7)² - (-0.4(5)²)) / (2)
= -4.800000000000001
Similarly, for function g(x) = -0.8x², the average rate of change over the interval 5 ≤ x ≤ 7 can be calculated as follows:
Average rate of change of g = (g(7) - g(5)) / (7 - 5)
= (-0.8(7)² - (-0.8(5)²)) / (2)
= -9.600000000000001
Comparing the average rates of change, we can see that function f(x) has an average rate of change of -4.800000000000001, while function g(x) has an average rate of change of -9.600000000000001. Since the average rate of change represents the slope of the secant line, this means that the secant line for function f(x) has a steeper slope than the secant line for function g(x).
Therefore, we can conclude that the average rate of change for function f(x) is steeper than the average rate of change for function g(x) over the interval 5 ≤ x ≤ 7.