The figure to the right shows the total sales, in thousands of dollars, from the

Question

The figure to the right shows the total sales, in thousands of dollars, from the distribution of x thousand catalogs. Find and interpret the average rate of changes of sales with respect to the number of catalogs distributed for the given changes in x. (a) 5 to 15 (b) 15 to 25 (c) 25 to 35 (d) What is happening to the average rate of change of sales as the number of catalogs distributed increases? (a) The average rate of change over 5 to 15 is (Type an integer or a simplified fraction.) This number implies that from catalog distributions of 5,000 to 15,000, sales will have an average of $ for each additional 1000 catalogs distributed. (b) The average rate of change over 15 to 25 is (Type an integer or a simplified fraction.) This number implies that from catalog distributions of 15,000 to 25,000, sales will have an average of $ for each additional 1000 catalogs distributed. (c) The average rate of change over 25 to 35 is (Type an integer or a simplified fraction.)

Explanation / Answer

Average rate of change = (Total change in that interval) / (Size of interval)

(a) From 5 to 15:

Total change = 35 - 25 = 10

Interval size = 15 - 5 = 10

Average rate of change = 10/10 = 1

This number implies that sales will have an average 1000 of $1 for each 1000 catalogs distributed.

(b) From 15 to 25:

Total change = 40 - 35 = 5

Interval size = 25 - 15 = 10

Average rate of change = 5/10 = 1/2

This number implies that sales will have an average 500 of $1 for each 1000 catalogs distributed.

(c) From 25 to 35:

Total change = 43 - 40 = 3

Interval size = 15 - 5 = 10

Average rate of change = 3/10

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