Question

1. the 2025 class is sponsoring a school dance. the function ( p(t)=8t - 200 ) models the profit ( p(t) ), in dollars, they will earn for the number of tickets, ( t ), that they sell. describe what each equation means.

a) ( p(20)=-40 )
b) ( p(25)=0 )
c) ( p(70)=360 )

Explanation:

• For \(P(20)= - 40\): When \(t = 20\) (20 tickets are sold), the profit \(P(t)\) is \(-40\) dollars. This means the class is at a loss of \(40\) dollars.
• For \(P(25)=0\): When \(t = 25\) (25 tickets are sold), the profit \(P(t)\) is \(0\) dollars. This is the break - even point, where the class neither makes a profit nor incurs a loss.
• For \(P(70)=360\): When \(t = 70\) (70 tickets are sold), the profit \(P(t)\) is \(360\) dollars. This means the class makes a profit of \(360\) dollars.

Answer:

A. When 20 tickets are sold, the class has a loss of 40 dollars.
B. When 25 tickets are sold, the class breaks even (neither makes a profit nor incurs a loss).
C. When 70 tickets are sold, the class makes a profit of 360 dollars.