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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. $\newline$ What is the domain of $P(t)$ ? $\newline$ Choices: $\newline$ (A) all real numbers from $0$ to $200$ $\newline$ (B) all whole numbers $\newline$ (C) all real numbers $\newline$ (D) all whole numbers from $0$ to $200$

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Domain and range of linear functions: word problems

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Q. 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.

\newline

What is the domain of

P(t)

?

\newline

Choices:

\newline

(A) all real numbers from

0

to

200

\newline

(B) all whole numbers

\newline

(C) all real numbers

\newline

(D) all whole numbers from

0

to

200

Define domain of function: The domain of a function is the set of all possible input values (independent variable) which allows the function to work within the context of the problem. In this case, the independent variable is the number of tickets sold, represented by $t$ .
Determine maximum capacity: The theater has a maximum capacity of $200$ people, which means the theater cannot sell more than $200$ tickets for the matinee showing. Therefore, the maximum value for $t$ is $200$ .
Identify minimum number of tickets: Since the theater cannot sell a fraction of a ticket, the minimum number of tickets that can be sold is $0$ , and $t$ must be a whole number. Therefore, the minimum value for $t$ is $0$ .
Establish domain of $\newline$ $P(t)$ : The domain of $\newline$ $P(t)$ is all the whole numbers from the minimum number of tickets that can be sold ( $\newline$ $0$ ) to the maximum number of tickets that can be sold ( $\newline$ $200$ ), inclusive. This means the domain of $\newline$ $P(t)$ is all whole numbers from $\newline$ $0$ to $\newline$ $200$ .

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