Question

A stadium that seats 35,000 is slowly filling up with fans. The game starts at four o’clock. At noon the stadium owner estimates there are 4,000 fans who have already arrived early. At one o’clock he estimates just over 11,000 fans have found their seats and they appear to be coming in at a steady rate. He knows his stadium will be more than ninety percent full by game time. Choose the function below that best models this situation and tracks attendance from Noon to game time.
A. f(x)= .90x + 4,000
B. f(x)= 7,000x + 4,000
C. f(x)= 4,000x + 4,000
D. f(x)= 11,000x + 4,000

Answer 1

Answer:

B. f(x) = 7000x + 4000

Step-by-step explanation:

To find the best function for this situation, we need to list down all the things that we know first.

We currently have:

35000 total seats

4000 fans

11000 fans after an hour

So that means that after an hour, we had:

11000 fans - 4000 fans = 7000 fans

At one o'clock we had 7000 more fans arrive.

So we can assume that:

x = number of hours

f(x) = 7000x + 4000 will be the best function to use to find out if there that 90% of the stadium will be filled by game time.

To test this function let's use it:

f(1) = 7000(1) + 4000

f(1) = 11000

This is after hour 1.

Now let's see after hour 4 since the game starts at 4.

f(4) = 7000(4) + 4000

f(4) = 28000 + 4000

f(4) = 32000

So 90% of 35000 is:

35000 x 0.90 = 31500

By game time we have 32000 fans which is above 90% of the total number of seats.

So the stadium owners estimate is correct.