Hello, Cockchestner007!

Three students wrote an adventure travel guidebook for Alberta and BC.

Two local publishers are interested in marketing it and both anticipate retailing the book for $20.

Publisher "A" offers a straight royalty of 10% (on the retail price) on all book sales.

Publisher "B" offers an 8% royalty for any books sold up to 5,000 copies

and will then increase the royalty to 15% for any copies sold in excess of 5,000.

a) Describe the type of function that will model the authors' income offered by each publisher.

Publisher A: The authors get for each book sold.

. . . . . . . . . This is a linear function.

Publisher B: The authors get for each book sold up to 5,000 books.

. . . . . . . . . They get for each book in excess of 5,000.

. . . . . . . . . This is a lnearfunction.piecewise

Let = number of books sold.b) Find the functions and

. . Note that function is a piecewise-defined function.

Publisher A: .

Publisher B: this is quite tricky.

For sales up to 5,000, they get: . per book.

. .

For sales in excess of 5,000, they get: . per book.

. .

If , they still get $1.60 for the first 5000 books: 8,000 dollars,

. . plus $3 each for all books over 5000: dollars.

Hence, for dollars.

Therefore: .