Question
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(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
UBMIT ANSWER

Ask by Moran Robbins. in the United States
Jan 31,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The net change in from to is -432. The average rate of change is -36 units per unit .

Solution

Let’s analyze the function over the interval from to .

(a) Net Change

The net change in the function between and is calculated as the difference between the value of the function at and .
  1. Calculate :
  2. Calculate :
  3. Determine the Net Change:
Interpretation: The function decreases by 432 units when increases from -6 to 6.

(b) Average Rate of Change

The average rate of change of over the interval from to is found by dividing the net change by the change in .
  1. Change in :
  2. Average Rate of Change:
Interpretation: On average, the function decreases by 36 units per unit increase in over the interval from -6 to 6.

Summary:

  • (a) The net change in from to is .
  • (b) The average rate of change of over this interval is units per unit .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

To determine the net change of the function between and :
First, calculate and .
Next, find the net change:
Now for the average rate of change:
Thus, the answers are:
(a) Net change:
(b) Average rate of change:

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