People start to leave the stadium at the end of a football game. The number of people, PP, that are left in the stadium mm minutes after the end of the game is given by the equation above. How many people were present when the game ended but before people started to leave?
The equation clearly says that
> There were 45,000 people at the end of the game
> Then they started to leave at the rate of 1000 people leaving per minute
This is an example of
y = mx + b
y = the number of people after any given minute
m = the rate of leaving (minus 1000 people per minute, the slope, the speed at which the population falls off)
x = the number of minutes, the variable (you plug in any number of minutes you are interested in)
b = the y intercept, the population of the stadium at the start of the problem, just at the beginning of the outflow.
In this case, the equation is:
y = mx + b
p = – 1000*number of minutes + 45000 people to start
P = – 1000x + 45,000
– same as –
P = 45,000 – 1000x
“The number of people remaining” equals “45,000” minus “1000 people per minute”
At a rate of leaving of 1000 leaving per minute, then at the end of 10 minutes (for example), ten thousand people would have left, and the population in the stadium would be down to 35,000 people.
To empty the stadium completely, it would take 45 minutes at a rate of 1000 per minute for 45 thousand people to leave.
To answer your question:
How many people are in the stadium before they start to leave?
All of them.
No one has left yet.
Before they start to leave, there are 45,000 people in the stadium.
Then after one minute, there are “45,000 people” minus “the first 1000 people to leave.”
After 2 minutes, 2000 people have left.
After 3 minutes, 3000 people have left.