Question

A new movie theater opens at the local mall. During the first month, the owner collected information
on how many customers they had throughout each day. The owner concluded that the number of
customers the theater has at any given moment can be represented by C(x) = -x2 + 11x where x
represents the number of hours that the movie theater has been open on a given day. The theater
opens at 12:00 PM.
At what time does the theater have no customers?
a.
11:00 PM
b. 5:30 PM
c. 2:00 PM
d. 8:30 PM

Answer 1

The time at which the theatre does not have any customers is; Choice A: 11:00 PM

Functions and variable

From the task content;

• The function which represents the number of customers the theater has at each point in time is;

• C(x) = -x² + 11x

Hence, when C(x) = 0, the theater has no customers.

• 0 = -x² +11x

Divide through by x;

• 0 = -x +11

x = 11.

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