A tennis club offers two payment options. Members can pay a monthly fee of $30 plus $5 per hour for court rental time. The second option has no monthly fee, but court time costs $7.50 per hour.
a. Write a mathematical model representing total monthly costs for each option for x hours of court rental time.
b. Use a graphing utility to graph the two models in a [0, 15, 1] by [0, 120, 20] viewing rectangle.
c. Use your utility’s trace or intersection feature to determine where the two graphs intersect. Describe what the coordinates of this intersection point represent in practical terms.
d. Verify part (c) using an algebraic approach by setting the two models equal to one another and determining how many hours one has to rent the court so that the two plans result in identical monthly costs.