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An amusement park prices tickets at [tex]$\$55$[/tex] and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing, that a [tex]$\[tex]$2$[/tex][/tex] increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.
Management uses the combined function [tex]$P$[/tex] to model the daily earnings of the amusement park, where [tex]$x$[/tex] is the number of [tex][tex]$\$[/tex]2$[/tex] increases in the price of a ticket.
[tex]P(x) = -40x^2 - 100x + 27,500[/tex]
Use the given information to complete the sentences.
The constant of the polynomial expression represents the ________. The binomial [tex]$(500 - 20x)$[/tex] is a factor of the polynomial expression and represents the ________.
The constant of the polynomial expression represents the initial daily earnings. The binomial [tex]\((500-20x)\)[/tex] is a factor of the polynomial expression and represents the average number of tickets sold after [tex]\( x \)[/tex] $2 increases in the price of a ticket.
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