QQuestionMathematics
QuestionMathematics
Which situation shows a constant rate of change?
A. The number of points scored in a basketball game compared with the number of minutes played.
B. The height of a monkey swinging from branch to branch over time.
C. The height of a bouncing ball over time.
D. The amount a person pays for gas compared with the number of gallons purchased.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the concept of constant rate of change
A constant rate of change means that the dependent variable changes at a uniform, consistent rate relative to the independent variable. This creates a straight line when graphed.
Step 3:: Analyze Option A - Points scored vs. minutes played
- In basketball, points are typically scored in discrete amounts (2 or 3 points at a time) - The points scored do not increase uniformly with each minute - This is NOT a constant rate of change
Step 4:: Analyze Option B - Monkey's height over time
- A monkey swinging between branches would have a variable height - The height would change irregularly as the monkey moves - This is NOT a constant rate of change
Step 5:: Analyze Option C - Bouncing ball height
- A bouncing ball's height changes non-linearly - Each bounce reduces the maximum height - The height is not consistent over time - This is NOT a constant rate of change
Step 6:: Analyze Option D - Gas purchased vs. amount paid
- $$\text{Cost} = \text{Price per gallon} \times \text{Number of gallons}
- As more gallons are purchased, the cost increases proportionally - This creates a straight line on a graph - This IS a constant rate of change
Final Answer
The amount a person pays for gas compared with the number of gallons purchased shows a constant rate of change.
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