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In order to plan for the future water supply, the average population of the world is needed. If the world population in 2015 was about billion people, determine the average population of the Earth during the next years. Assume the population, in billions, years from 2015 is projected to be:

You are asked to determine the average value of , given the function itself. Which variation of Mean Value will you use?

Average (Mean) Values

To calculate the mean (average) value of a finite set of items, add up the values of items and divide by the number of items.

Integrals help us add over a continuous interval. Therefore, for any continuous function :

mean value of over

Since , we can also calculate the average value of any function using its antiderivative . Its average slope gives the average rate of change of , which is the same as the average value of

  mean rate of change of over