The amount of fans that have entered the stadium of a UT football game after the doors have opened is shown in the table below.
t (minutes) attendance
10 40,000
20 60,000
30 70,000
40 80,000
50 85,000
60 90,000
70 95,000
80 100,000
Looks like the attendance is really "stadium-tacular"! It's rising like a quarterback throwing a touchdown pass. With each passing minute, more and more fans are piling into the stadium like clowns into a tiny car. It's like a circus in there, but with football instead of juggling!
To determine the average rate of change of attendance at the UT football game, we need to find the change in attendance divided by the change in time.
First, let's find the change in attendance from the beginning to the end of the given time interval.
The attendance at the beginning (t = 10 minutes) is 40,000.
The attendance at the end (t = 80 minutes) is 100,000.
Therefore, the change in attendance is 100,000 - 40,000 = 60,000.
Next, let's find the change in time.
The time at the beginning is 10 minutes.
The time at the end is 80 minutes.
Therefore, the change in time is 80 - 10 = 70 minutes.
Now, we can calculate the average rate of change of attendance by dividing the change in attendance by the change in time.
Average rate of change = (change in attendance) / (change in time)
Average rate of change = 60,000 / 70
Average rate of change ≈ 857.14 fans per minute.
Therefore, the average rate of change of attendance at the UT football game is approximately 857.14 fans per minute.
To analyze the attendance data for a UT football game, we can observe the table provided. It shows the number of fans that have entered the stadium at different times after the doors have opened.
To find the rate at which fans are entering the stadium, we can calculate the average rate of change of attendance over time. The average rate of change measures how the attendance is changing on average during a certain time interval.
To find the average rate of change between any two given times, we can use the formula:
Average Rate of Change = (Change in Attendance) / (Change in Time)
Let's calculate the average rate of change between the first and last time intervals given in the table:
Change in Attendance = Final Attendance - Initial Attendance
Change in Time = Final Time - Initial Time
Using the table, we can calculate:
Change in Attendance = 100,000 - 40,000 = 60,000
Change in Time = 80 - 10 = 70 minutes
Now, we can substitute these values into the formula for average rate of change:
Average Rate of Change = (60,000) / (70)
Therefore, the average rate of change of attendance over the first 70 minutes is approximately 857 fans per minute.
This calculation tells us that, on average, around 857 fans are entering the stadium every minute during the first 70 minutes after the doors are opened.
looks like either a square root or as log
Note how its rate of increase keeps decreasing