Question
Julissa and Andrew have set up a movie theater in their basement and are selling tickets to their friends. They had to spend $25 to buy the materials for the tickets and set up the basement. They plan to charge $5 per ticket. What kind of function best models their profit based on each number of tickets they could sell?
Option #1: linear function
Option #2: quadratic function
Option #3: exponential function
Option #4: periodic function
(1 point)
Option #1: linear function
Option #2: quadratic function
Option #3: exponential function
Option #4: periodic function
(1 point)
Answers
GPT-4o mini
The best function to model Julissa and Andrew's profit based on the number of tickets they sell is a **linear function** (Option #1).
Here's why:
- The profit can be calculated with the formula: Profit = Revenue - Costs.
- They charge $5 per ticket, so the revenue from selling \( n \) tickets is \( 5n \).
- Their initial costs are $25. Therefore, the profit function is:
\[ \text{Profit} = 5n - 25 \]
This function is linear because it has the form \( y = mx + b \) where \( m \) (the slope) is constant, and \( b \) (the y-intercept) represents the initial costs.
Hence, as the number of tickets sold increases, profit increases linearly.
Here's why:
- The profit can be calculated with the formula: Profit = Revenue - Costs.
- They charge $5 per ticket, so the revenue from selling \( n \) tickets is \( 5n \).
- Their initial costs are $25. Therefore, the profit function is:
\[ \text{Profit} = 5n - 25 \]
This function is linear because it has the form \( y = mx + b \) where \( m \) (the slope) is constant, and \( b \) (the y-intercept) represents the initial costs.
Hence, as the number of tickets sold increases, profit increases linearly.