Packet #4 Average Rate of Change

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Presentation transcript:

Packet #4 Average Rate of Change Math 160 Packet #4 Average Rate of Change

If you drive 100 miles in 2 hours, what’s your average speed

If you drive 100 miles in 2 hours, what’s your average speed 50 mph

Average speed

Average speed

Average speed

Average rate of change

The average rate of change of the function 𝑦=𝑓(𝑥) between 𝑥=𝑎 and 𝑥=𝑏 is average rate of change= Δ𝑦 Δ𝑥 = change in 𝑦 change in 𝑥 = 𝑓 𝑏 −𝑓 𝑎 𝑏−𝑎

Note: The average rate of change is also the slope of the secant line.

Note: The average rate of change is also the slope of the secant line.

Ex 1. Find the average rate of change of 𝑓 𝑥 =1−3 𝑥 2 between 𝑥=−2 and 𝑥=0.

Ex 1. Find the average rate of change of 𝑓 𝑥 =1−3 𝑥 2 between 𝑥=−2 and 𝑥=0.

Ex 1. Find the average rate of change of 𝑓 𝑥 =1−3 𝑥 2 between 𝑥=−2 and 𝑥=0.

Here are the U.N.’s 2012 medium projections of the world’s population. Ex 2. Here are the U.N.’s 2012 medium projections of the world’s population. What is the average rate of change of population between 2010 and 2030? What was the average rate of change of population between 2030 and 2050? Year World Population (in millions) 2010 6,916 2020 7,717 2030 8,425 2040 9,039 2050 9,551 2060 9,957

Here are the U.N.’s 2012 medium projections of the world’s population. Ex 2. Here are the U.N.’s 2012 medium projections of the world’s population. What is the average rate of change of population between 2010 and 2030? What is the average rate of change of population between 2030 and 2050? Year World Population (in millions) 2010 6,916 2020 7,717 2030 8,425 2040 9,039 2050 9,551 2060 9,957

Source: Wikipedia

Note: Linear functions have a constant rate of change Note: Linear functions have a constant rate of change. This makes sense because the slope of any secant line (that is, the average rate of change) will be the slope of the linear function. For example, the rate of change of 𝑓 𝑥 =−2𝑥+3 is ____.

Note: Linear functions have a constant rate of change Note: Linear functions have a constant rate of change. This makes sense because the slope of any secant line (that is, the average rate of change) will be the slope of the linear function. For example, the rate of change of 𝑓 𝑥 =−2𝑥+3 is ____.

Note: Linear functions have a constant rate of change Note: Linear functions have a constant rate of change. This makes sense because the slope of any secant line (that is, the average rate of change) will be the slope of the linear function. For example, the rate of change of 𝑓 𝑥 =−2𝑥+3 is ____.

Note: Linear functions have a constant rate of change Note: Linear functions have a constant rate of change. This makes sense because the slope of any secant line (that is, the average rate of change) will be the slope of the linear function. For example, the rate of change of 𝑓 𝑥 =−2𝑥+3 is ____. −𝟐