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:
[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
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