The maximum occupancy of a concert hall is 1,200 people. The hall is hosting a concert, and 175 people enter as soon as the doors open in the morning. The number of people coming into the hall then increases at a rate of 30% per hour. If t represents the number of hours since the doors open, which inequality can be used to determine the number of hours after which the amount of people in the concert hall will exceed the occupancy limit?
A. 175(1.30)^t > 1200
B. 175(0.70)^t < 1200
C. 175(0.30)^t < 1200
D. 175(1.03)^t > 1200
The initial number of people in the concert hall is 175. Since the number of people coming into the hall increases at a rate of 30% per hour, we can represent the number of people in the hall after t hours as 175(1 + 0.30)^t.
To determine the number of hours after which the amount of people in the concert hall will exceed the occupancy limit (1200), we need to find the value of t that satisfies the inequality:
175(1 + 0.30)^t > 1200
Simplifying this inequality, we get:
175(1.30)^t > 1200
Therefore, the answer is choice A.