Math Problem Statement
Solution
To calculate the average rate of change of the function on the interval from to , we will use the formula for the average rate of change:
In this case:
- and
- We need to find and from the graph.
From the graph:
- (the height at time )
- (the height at time )
Now we substitute these values into the formula:
Thus, the average rate of change is feet per second.
Would you like further details or have any questions?
Here are 5 related questions:
- How is the average rate of change related to the slope of a line?
- What does the negative sign in the rate of change signify in this context?
- How can you determine the rate of change from a table of values?
- What happens to the rate of change when the slope of the graph is horizontal?
- How would you calculate the rate of change over a different interval, say from to ?
Tip: The rate of change in a linear graph is constant, so the slope remains the same across the entire line.
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Math Problem Analysis
Mathematical Concepts
Average Rate of Change
Linear Functions
Slope
Formulas
Average rate of change = (f(x2) - f(x1)) / (x2 - x1)
Theorems
Slope of a Linear Function
Suitable Grade Level
Grades 8-10
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