Section 11.1

Average Rate of Change

In this section, we’ll examine how quantities change with respect to each other. This is a topic that is not entirely unfamiliar. On a long trip in a car, you may be interested in knowing how the distance traveled changes with respect to how much time has elapsed. By knowing how many miles per hour your vehicle has averaged, you get an idea of how long it will take you to arrive at your destination.

Auto manufacturers are also interested in how far a vehicle will travel, but as the amount of gasoline that is in the tank changes. By comparing the distance traveled to the amount of gasoline consumed, they get an idea of how efficient the vehicle is. Vehicles that achieve a higher miles per gallon are more efficient than those that achieve a lower miles per gallon.

An insurance analyst might be interested in knowing how the percentage of people who are driving uninsured varies as the percentage of people who are unemployed changes. By understanding how these percentages vary with respect to each other, they can better understand the risk of being in an accident with a person who is uninsured.

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