Scott and Ian design a cool T-shirt for snow boarders. Their friends are very impressed and everybody wants one, so Scott and Ian set up a T-shirt printing business in their garage. Total start-up costs are $450 due to the availability of a used graphics machine. They estimate that it costs them $5.50 to print each T-shirt. If x is the number of T-shirts produced, then the cost of producing x shirts is given by and the average cost of producing x T-shirts is given by .
a) Find the equation for horizontal asymptote for y = A(x). (1 mark)
b) Explain why the value for the height of the horizontal asymptote in (a) makes sense in the real-life context of this problem. Be clear and concise. (2 marks)
c) Use the function to prove that the average cost per shirt never reaches $5.50 per shirt. Your answer should include both algebra and reasoning. (3 marks)