Question

H(t)=(t⋅3)²⋅5

What is the average rate of change of h over the interval −5≤t≤−1?

Answer 1

The average rate of change of the function h(t) over the interval -5 to -1 is calculated by finding the values of h(-5) and h(-1), and then using the formula for average rate of change, which results in -495.

Step-by-step explanation:

The average rate of change of a function h(t) = (t \cdot 3)^2 \cdot 5 over an interval from a to b is given by the formula \((h(b) - h(a)) / (b - a)\). To find the average rate of change of h over the interval -5 ≤ t ≤ -1, we first compute h(-5) and h(-1).

For h(-5), we plug in t = -5 into h(t): h(-5) = ((-5) \cdot 3)^2 \cdot 5 = 45^2 \cdot 5. For h(-1), we substitute t = -1: h(-1) = ((-1) \cdot 3)^2 \cdot 5 = 9 \cdot 5.

Now, calculate h(-5) and h(-1):

• h(-5) = 2025
• h(-1) = 45

We then use these values to find the average rate of change:

Average Rate of Change = (h(-1) - h(-5)) / (-1 - (-5))

Average Rate of Change = (45 - 2025) / 4

Average Rate of Change = -1980 / 4

Average Rate of Change = -495

The average rate of change of the function h over the interval -5 ≤ t ≤ -1 is -495.