Three students in an outdoor pursuits program collaborated to write an adventure travel guidebook for Alberta and BC. Two local publishers are interested in marketing and publishing 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 be used to model the author income offered by each publisher.

b) Find the functions A(x) and B(x). Notice that function A(x) is a piecewise-defined function.