Math 111: Exam 02 Solutions - Blake Farman - University Of South Carolina

Math 111: Exam 02 Solutions - Blake Farman - University Of South Carolina - 2013 Page 5

MATH 111: EXAM 02 SOLUTIONS

Using the second, we distribute on the right hand side and add 25 to both sides to get

y = 7x

35 + 25 = 7x

10.

9 (16 Points). Alice is hosting an event. She is renting a facility, which costs $300, and

providing refreshments, which cost $4 per guest.

(a) Find a function, C, that models the total cost of the event if x people attend.

(b) Sketch a graph of C.

(d) If the total cost for the event was 400, how many people attended?

Solution. (a) Since the $300 to rent the facility is paid even if no guests attend, this is our

initial value for the cost function. We know that each additional guest increases the cost

of the event by $4, so our cost function is

C(x) = 4x + 300.

(b) Below is a plot of the function. Note that it does not include portions where x < 0 since

there is no reasonable meaning for a negative number of guests.

C(10) = 4(10) + 300 = 40 + 300 = 340.

This models the cost of the event if 10 guests attend. When x = 15 we have

C(15) = 4(15) + 300 = 60 + 300 = 360.

This models the cost of the event if 15 guests attend.

Math 111: Exam 02 Solutions - Blake Farman - University Of South Carolina - 2013 Page 5