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
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To find the rate at which fans are entering the stadium after the doors have opened, we need to determine the average rate of change in attendance with respect to time. This can be done by calculating the slope of the line that passes through two points on the attendance-time graph.
First, let's select two points from the given data. We can choose the points (10, 40,000) and (60, 90,000). These points represent the attendance at 10 minutes and 60 minutes, respectively.
Next, we can use the slope formula, which is given by:
slope = (change in y) / (change in x)
where change in y denotes the difference in attendance values and change in x denotes the difference in time values.
So, using the selected points, we have:
change in y = 90,000 - 40,000 = 50,000
change in x = 60 - 10 = 50
Now, we can calculate the slope by dividing the change in y by the change in x:
slope = 50,000 / 50 = 1,000 fans per minute
Therefore, the rate at which fans are entering the stadium after the doors have opened is 1,000 fans per minute.