Question

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)

Answer 1

Polynomials are algebraic expressions represented by variables and coefficients.

(a) How to determine the interval the open seats increased

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)

(b) The time the first meeting ended

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

(c) When there were 700 open seats

From the graph, we have:

(x,y) = (5, 700)

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

(d) The average rate of change from 10:00 AM to 10:25 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:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

This gives

$m = \frac{100 - 800}{25 - 0}$

$m = \frac{-700}{25 }$

$m = -28$

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

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