HURRY PLEASE PLEASE
A high school auditorium is used for two meetings over the 100 minutes. The polynomial
function p(x) models the number of open seats in the auditorium from 10 A.M. (when x = 0)
to 11:40 A.M. (when x = 100)

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MrRoyalid MrRoyalid · Answer 1

Polynomials are algebraic expressions represented by variables and coefficients.

This is the interval, where the open seats increase the same time the time in minutes increases.

From the graph, the open seats increases at the interval (100, 600)

This is the first point where the curve changes its direction from decreasing values to increasing values

From the graph, the curve changes its direction at point (25,100)

Hence, the first meeting ended at 10:25 AM

From the graph, we have:

(x,y) = (5, 700)

Hence, there were 700 open seats at 10:05 AM

At 10:00 AM, we have:

(x,y) = (0,800)

At 10:25 AM, we have:

(x,y) = (25,100)

So, the average rate of change is:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

This gives

[tex]m = \frac{100 - 800}{25 - 0}[/tex]

[tex]m = \frac{-700}{25 }[/tex]

[tex]m = -28[/tex]

Hence, the average rate of change from 10:00 AM to 10:25 AM is -28 people per minute