the juniper street theater offers a special movie matinee showing every sunday morning. the theater, which…

the juniper street theater offers a special movie matinee showing every sunday morning. the theater, which has a maximum capacity of 200 people, sells matinee tickets for $5 each. the function p(t) represents the theater’s revenue, in dollars, for selling t tickets. what is the domain of p(t)? all real numbers from 0 to 200 all whole numbers from 0 to 200 all real numbers all whole numbers

the juniper street theater offers a special movie matinee showing every sunday morning. the theater, which has a maximum capacity of 200 people, sells matinee tickets for $5 each. the function p(t) represents the theater’s revenue, in dollars, for selling t tickets. what is the domain of p(t)? all real numbers from 0 to 200 all whole numbers from 0 to 200 all real numbers all whole numbers

Answer

Explanation:

Step1: Understand the problem context

The function ( P(t) ) represents the theater's revenue from selling ( t ) tickets. The theater has a maximum capacity of 200 people, so ( t ) (number of tickets sold) can't be negative and can't exceed 200. Also, the number of tickets sold must be a whole number (you can't sell a fraction of a ticket).

Step2: Analyze the domain options

  • "all real numbers": Incorrect, because you can't sell a negative number of tickets or a fraction of a ticket, and there's a maximum of 200.
  • "all real numbers from 0 to 200": Incorrect, same reason as above—tickets sold must be whole numbers, not all real numbers in that interval.
  • "all whole numbers from 0 to 200": Correct, because ( t ) (number of tickets) must be a whole number (0, 1, 2, ..., 200) since you can't sell a negative or fractional number of tickets, and the maximum capacity is 200.
  • "all whole numbers": Incorrect, because you can't sell more than 200 tickets (due to maximum capacity).

Answer:

all whole numbers from 0 to 200