At the start of a new movie at the Cineplex 16, there are 250 people in the theater. However, 10% of the people walk out of the theater within the first 15 minutes of the movie starting. If another 10% leave in the next 15 minutes and this rate continues for the duration of the movie, which of the following graphs correctly models the number of people in the theater during the movie?
A.
B.
C.
D.
Answer:A
At the start of a new movie at the Cineplex 16, there are 250 people in the theater. However, 10% of the people walk out of the theater within the first 15 minutes of the movie starting. If another 10% leave in the next 15 minutes and this rate continues for the duration of the movie, which of the following graphs correctly models the number of people in the theater during the movie?
A. B. C. D.
Explanation: AYou can start with Process of Elimination. Since the number of people in the theater decreases over time, you can eliminate (D). Choices (A) and (B) are exponential functions, whereas (C) is linear. The number of people that leave the theater every 15 minutes is not constant, since it is proportional to the number of people currently in the theater; therefore, this function is not linear, and you can eliminate (C). Choice (A) must be correct since the function decreases quickly and then the number leaving every successive 15 minutes is less than the time before (10% of 250 is more than 10% of 225).