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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?

Respuesta :

The answer is

175(1.30)t > 1,200

Answer:

Step-by-step explanation:

Given that the maximum occupancy of a concert hall is 1,200 people.  

For the concert hosted by the hall, 175 people are said to enter at the time of opening of the hall.

Afterwards every hour 30% increases.

i.e. 175 (1.3)

In other words in 0 hour 175 people, in I hour 175 (1.3) in II hour 175 (1.3)^2 etc

If t is any time considered then the number of people at time t would be

[tex]175(1.3)^t, t=1,2,3,....[/tex]

At time t total number of people inside the hall would be

[tex]170 \Sigma_1^t  1.3^t[/tex]

Since total capacity is 1200 this sum cannot exceed 1200

Hence inequality is [tex]170 \Sigma_1^t  1.3^t\leq 1200[/tex]

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