Question

2. Suppose that in the sales tax example, we wanted the output to be the total cost of the piece of merchandise instead of just the tax. Let C be the name of the cost function. Use the sales tax rate that is in effect where you live. (If you happen to live in a location with no sales tax, use 8%.)

2. If you purchase a CD priced at $13.79, determine the total cost. Use functional notation to represent the cost.
3. If you purchase an item costing $59.95, determine the total cost. Use functional notation to represent the cost.
4. If the price of an item is P dollars, describe in words how you calculate C(P), the cost of the item.
5. Determine a formula for C(P). Simplify your formula as much as possible.

Answer 1

1. If C is the cost function, then we have the equation of the function as
C(P) = P + 0.08P
P is the tax-free sales cost
we use 8% tax rate


3. If the price is $13.79
C($13.79) = 1.08 ($13.79) = $14.89

4. If the price is $59.95
C($59.95) = 1.08 ($59.95) = 64.75

5. C(P) = P + 0.08P
Simplifying,
C = 1.08P