Final answer:
To find the average rate of change of g(t) over the interval -4 ≤ t ≤ 5, calculate the change in g(t) divided by the change in t. Use the given equation g(t) = -(t-1)² + 5 to find the corresponding values of g(t) and apply the formula.
Step-by-step explanation:
The average rate of change of g(t) over the interval -4 ≤ t ≤ 5 can be found by calculating the change in g(t) divided by the change in t. We can plug in the values of t and calculate the corresponding values of g(t) using the given equation g(t) = -(t-1)² + 5. Then we can find the average rate of change using the formula (g(5) - g(-4)) / (5 - (-4)).
By substituting the values, we get (-(5-1)² + 5 - (-(4-1)² + 5)) / (5 - (-4)). Simplifying further, we get (-16 - (-27)) / 9 = 11/9.