t g(t) -5 6 -4 4 -3 2 -2 1 -1 -1 0 -2 1 -3 2 1 3 3 4 6 5 9 what is the average rate of change of g over the…

t g(t) -5 6 -4 4 -3 2 -2 1 -1 -1 0 -2 1 -3 2 1 3 3 4 6 5 9 what is the average rate of change of g over the interval -4 ≤ t ≤ 1? give an exact number. related content worked example: average rate of change from graph

t g(t) -5 6 -4 4 -3 2 -2 1 -1 -1 0 -2 1 -3 2 1 3 3 4 6 5 9 what is the average rate of change of g over the interval -4 ≤ t ≤ 1? give an exact number. related content worked example: average rate of change from graph

Answer

Explanation:

Step1: Find the values of (g(t)) at the endpoints

When (t = - 4), (g(-4)=4). When (t = 1), (g(1)=-3).

Step2: Use the average rate of change formula

The formula for the average rate of change of a function (y = g(t)) over the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here, (a=-4), (b = 1). So, (\frac{g(1)-g(-4)}{1-(-4)}=\frac{-3 - 4}{1 + 4}).

Step3: Calculate the result

(\frac{-3-4}{1 + 4}=\frac{-7}{5}=-1.4)

Answer:

(-1.4)