Question

select the correct answer.
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(0.30)^t < 1,200
b. 175(1.30)^t > 1,200
c. 175(1.03)^t > 1,200
d. 175(0.70)^t < 1,200

Explanation:

Step1: Identify the growth factor

The number of people increases at a rate of 30% per hour. The growth factor for a percentage increase of \(r\) is \(1 + r\). Here, \(r=0.30\), so the growth factor is \(1 + 0.30=1.30\).
The initial number of people is 175. The formula for the number of people after \(t\) hours is \(N = 175(1.30)^{t}\).

Step2: Set up the inequality

We want to find when the number of people \(N\) exceeds 1200. So the inequality is \(175(1.30)^{t}>1200\).

Answer:

B. \(175(1.30)^{t}>1200\)