Question

question
gates open for a football game at the central stadium at 7 p.m. (time t = 0 minutes) with 28,900 people in line waiting to get in and 0 people inside. at 7:31 p.m. (time t = 31 minutes), there are 3,400 people in line still waiting and 25,500 people inside the stadium. find the average rate of change in number of people waiting in line from t = 0 to t = 31 minutes, rounding your answer to three decimal places, with appropriate units. then fill in the guided sentence below to interpret the meaning of your answer in context.
answer
the average rate of change is
it represents that the
is
at a rate of
over that time interval.

Explanation:

Step1: Identify the initial and final values

Initial number of people in line $y_1 = 28900$, final number of people in line $y_2=3400$, initial time $x_1 = 0$, final time $x_2 = 31$.

Step2: Use the average - rate - of - change formula

The formula for the average rate of change is $\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $\frac{3400 - 28900}{31-0}=\frac{- 25500}{31}\approx - 822.581$.

Answer:

The average rate of change is $-822.581$ people per minute. It represents that the number of people in line is decreasing at a rate of $822.581$ people per minute over that time interval.