the revenue from selling movie tickets is giv...
the revenue from selling movie tickets is given by the function r(t) = 10t, where \t\ is the number of tickets sold. the theater holds a maximum of 200 people. the profit is a function of the revenue \r\ and is given by the function p(r) = 0.20r. what is the domain of the profit function p(r)? a {0, 1, 2, 3, ..., 200} b {0, 10, 20, 30, ..., 2000} c {any nonnegative real number ≤ 200} d {any nonnegative real number ≤ 2000}
Answer
# Explanation:
## Step1: Find the revenue - ticket relationship
The revenue function is $R(t)=10t$, where $t$ is the number of tickets sold and $0\leq t\leq200$ (since the theater holds a maximum of 200 people).
## Step2: Find the range of the revenue function
When $t = 0$, $R(0)=10\times0 = 0$. When $t = 200$, $R(200)=10\times200=2000$. So, the revenue $R$ ranges from $0$ to $2000$, i.e., $0\leq R\leq2000$.
## Step3: Determine the domain of the profit function
The profit function is $P(R) = 0.2R$. The domain of $P(R)$ is the set of all possible values of $R$. Since $R$ (revenue) ranges from $0$ to $2000$, the domain of $P(R)$ is any non - negative real number $\leq2000$.
# Answer:
D. {any non - negative real number $\leq2000$}