Question

adium people are exiting a soccer stadium at a constant rate after the game has ended. the graph shows the number of people in the stadium x minutes after game has ended. use the graph to estimate the x- and y-intercepts of the function and interpret the meanings in the context of the situation.

Explanation:

Step1: Find y - intercept

The y - intercept is the point where \(x = 0\). From the graph, when \(x = 0\) (at the start, when the game just ended), the number of people \(y=4000\). So the y - intercept is \((0, 4000)\). In the context, this means that when the game has just ended (\(x = 0\) minutes after the game ended), there are 4000 people in the stadium.

Step2: Find x - intercept

The x - intercept is the point where \(y = 0\). From the graph, when \(y = 0\) (no people left in the stadium), \(x = 60\). So the x - intercept is \((60, 0)\). In the context, this means that 60 minutes after the game has ended, there are 0 people left in the stadium (the stadium is empty).

Answer:

y - intercept: \((0, 4000)\), meaning 4000 people are in the stadium when the game ends (\(x = 0\) minutes). x - intercept: \((60, 0)\), meaning 60 minutes after the game ends, the stadium is empty.