Average Rate of Change.

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Presentation transcript:

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 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

Average Rate of Change using function notation

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

A. Find the rate of change from day 1 to 2. Ex 4 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. m = 11 Days (x) Amount of Bacteria f(x) 1 19 2 30 3 48 4 76 5 121 6 192 B. Find the rate of change from day 2 to 5.

Ex 5 Find the Average Rate of Change Households in Millions f(x) In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. Year (x) Households in Millions f(x) 2008 66 2009 61 2010 56 2011 51 m = -5 What does this mean? It decreased 5 million households per year from 2008 – 11.