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# The number $N$ of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of October 1 are given.)(a) Find the average rate of growth (i) from 2006 to 2008 (ii) from 2008 to 2010In each case, include the units. What can you conclude?(b) Estimate the instantaneous rate of growth in 2010 by taking the average of two average rates of change. What are its units?(c) Estimate the instantaneous rate of growth in 2010 by measuring the slope of a tangent.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So for the given problem we're looking at um the number of locations of a popular coffeehouse chain. Um So we want to find the average rate of growth from 2000 and 6 to 2008. So if we look at 2000 and eight um we see this is going to be 16,680. And then in 2000 and six there's 12,440. So we look at the change over the change in time. So the change in stores over the change in time, the change in time is two years. So we see that the average rate of growth is 2120 stores per year, and then from 2000 and 8, 2010, that's still a difference in two years. However, now this is going to be 16 six E and this is going to be 16 8 58 which only gives us an 89 increase. So we see that from 2000 and 6 to 2000 and eight there was a great greater rate of change on average.

California Baptist University

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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