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Average Rate of Change. Rate of Change. Ratio describing how one quantity changes as another quantity changes Slope can be used to describe it. Rate of Change. Positive – increases over time Negative – decreases over time. Rate of Change.
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Rate of Change • Ratio describing how one quantity changes as another quantity changes • Slope can be used to describe it
Rate of Change • Positive – increases over time • Negative – decreases over time
Rate of Change • Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time
Rate of Change • Exponential Functions do not have a constant rate of change, meaning that values increase or decrease at different rates over a period of time.
Rate of Change • Horizontal lines have 0 rate of change • Vertical lines have undefined rate of change
Ex 1 Find the Average Rate of Change f(x) = 2x2 – 3 from [2, 4].
Ex 2 Find the Average Rate of Change f(x) = 3x – 2 from [2, 5].
Ex 3 Find the Average Rate of Change f(x) = -4x + 10 from [-1, 3]. m = -4
Ex 4 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. m = 11 B. Find the rate of change from day 2 to 5.
Ex 5 Find the Average Rate of Change In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. m = -5 What does this mean? It decreased 5 million households per year from 2008 – 11.