SOLUTION: Please help me solve this problem: Jacob is the booking agent for a popular band. He has found that when he sells each ticket to a concert by the band for $63, the average attenda

Question 1041590: Please help me solve this problem:
Jacob is the booking agent for a popular band. He has found that when he sells each ticket to a concert by the band for $63, the average attendance for the concert is 24,305. In addition, Jacob has found that with every $20 increase in the ticket price, the average attendance for the concert decreases by an average of 1,202.
The band's profit per concert is given by the polynomial below, where x is the number of $20 increases in the ticket price over $63.
P(x) = $1,531,215 + $410,374x - $24,040x^2
What does the constant of polynomial P(x) represent?
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The constant is the profit the band makes when x=0, and that occurs when the ticket price is $63. As ticket prices increase, initially the profits increase, too, but eventually people stop buying the tickets at a rate that has the profits decrease.
It can be shown (not part of the answer needed) that when x= about 8.5, or an increase in ticket price of 8.5*20, or $170, the maximum revenue is obtained.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

P(x) is the profit when the ticket price is 63 + 20x dollars. What do you think P(0) means?

John

My calculator said it, I believe it, that settles it

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