Question

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?

Answer 1

Answer:

175[1+(30t/100)] > 1200

Step-by-step explanation:

The concert hall has a capacity of 1200 people.

Given that, 175 people enter the hall as soon as the door opened in the morning and after that people enter at an increasing rate of 30 % per hour.

Hence, after one hour of the doors opened the number of people in the hall will be 175(1+30/100).

Similarly, after two hours the number of people in the hall will be 175[1+(30×2/100)].

Then after t hours, the number of people in the hall will be 175[1+(30t/100)]

Hence, the inequality which determines the number of hours after which the number of people in the hall will exceed the occupancy limit will be

175[1+(30t/100)] > 1200 .  (Answer)