# Average Rate of Change Rate of Change Ratio

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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 • 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) = 2 x 2 – 3 from [2, 4].

Ex 2 Find the Average Rate of Change f(x) = 3 x – 2 from 2 ≤ x ≤ 5

Ex 3 Find the Average Rate of Change f(x) = -4 x + 10 from x 1= -1 x 2= 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. Days (x) Amount of Bacteria f(x) 1 19 2 30 3 48 4 76 5 121 6 192

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 Year (x) Households in Millions f(x) 2008 66 2009 61 2010 56 2011 51 What does this mean? It decreased 5 million households per year from 2008 – 11.