Average Rate of Change

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What is the average rate of change?

Back

The average rate of change is a measure of how a quantity changes over a specific interval. It is calculated as the change in the value of a function divided by the change in the input value.

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How do you calculate the average rate of change?

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To calculate the average rate of change between two points (x1, y1) and (x2, y2), use the formula: (y2 - y1) / (x2 - x1).

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What does a positive average rate of change indicate?

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A positive average rate of change indicates that the quantity is increasing over the interval.

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What does a negative average rate of change indicate?

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A negative average rate of change indicates that the quantity is decreasing over the interval.

Front

What is the average rate of change of a linear function?

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For a linear function, the average rate of change is constant and equal to the slope of the line.

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If a population increases from 1 million to 3 million over 10 years, what is the average rate of change?

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The average rate of change is (3 million - 1 million) / 10 years = 0.2 million people/year.

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What is the average rate of change in the context of a graph?

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In the context of a graph, the average rate of change represents the slope of the secant line connecting two points on the graph.

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How can average rate of change be applied in real life?

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Average rate of change can be used in various real-life situations, such as calculating speed, population growth, or changes in financial investments.

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What is the average rate of change between the points (2, 4) and (6, 16)?

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The average rate of change is (16 - 4) / (6 - 2) = 12 / 4 = 3.

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What is the significance of the average rate of change in calculus?

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In calculus, the average rate of change is a precursor to the concept of instantaneous rate of change, which is represented by the derivative.