15. A company called Blurb (http://www.blurb.com/volume printing) prints books.According to its advertisement, you get a 15% discount on all orders of 51 ormore copies of the same book (up to 100 copies). Is the cost per order a linearfunction of the number of copies you order (up to 100)?

A linear function is one in which the dependent variable (Cost per order) is directly proportional to the independent variable (Number of copies one orders). A linear function can also mirror the equation of a straight line.

The point is just that if a function is linear, there will be a direct relationship between its dependent and independent variables.

For this question, we are told that the cost per order depends on the number of books ordered. With a discount of 15% kicking in when the number of copies ordered is 51 or more.

In mathematical terms, if n books are ordered, and the cost of the order is c,

If n is less than 51, that is, n < 51,

c = kn (where k is a constant and it stands for the price of each book)

If n is equal to or more than 51, that is, n ≥ 51,

c = kn - (15% of kn)

c = kn - 0.15kn

c = 0.85kn

We can see that in the two cases, the cost of each order is still directly proportional to the number of copies ordered even though, the constant of proportionality in each of the two cases is different (k and 0.85k),

Hence, we can conclude that the cost per order is a linear function of the number of copies ordered (up to 100 at least)

Hope this Helps!!!