Question
A movie streaming service charges $10 up front and $2 for each movie thereafter. Which graph best represents the cost of watching movies over time?
Answers
GPT-4o mini
To represent the cost of watching movies over time for a streaming service that charges a $10 upfront fee and $2 for each subsequent movie, we can break down the cost as follows:
1. The initial cost is $10, which is charged upfront.
2. Each additional movie watched after the first one costs an additional $2.
The total cost can be calculated using the formula:
- For 0 movies watched: Cost = $10.
- For 1 movie watched: Cost = $10.
- For 2 movies watched: Cost = $10 + $2(1) = $12.
- For 3 movies watched: Cost = $10 + $2(2) = $14.
- For 4 movies watched: Cost = $10 + $2(3) = $16.
- And so on…
Graphically, the representation would be:
- The y-axis (vertical) represents the total cost.
- The x-axis (horizontal) represents the number of movies watched.
- The line starts at $10 (the cost for 0 movies) and remains horizontal until 1 movie is reached. After that point, the line will slope upwards, increasing by $2 for each additional movie watched.
The result will be a piecewise linear graph starting at $10 on the y-axis, remaining flat until the first movie, and then increasing linearly with a slope of 2 for every movie afterward.
Therefore, the best representation will have a horizontal line at $10 for the first movie, and after that, it will slope upwards in a straight line.
1. The initial cost is $10, which is charged upfront.
2. Each additional movie watched after the first one costs an additional $2.
The total cost can be calculated using the formula:
- For 0 movies watched: Cost = $10.
- For 1 movie watched: Cost = $10.
- For 2 movies watched: Cost = $10 + $2(1) = $12.
- For 3 movies watched: Cost = $10 + $2(2) = $14.
- For 4 movies watched: Cost = $10 + $2(3) = $16.
- And so on…
Graphically, the representation would be:
- The y-axis (vertical) represents the total cost.
- The x-axis (horizontal) represents the number of movies watched.
- The line starts at $10 (the cost for 0 movies) and remains horizontal until 1 movie is reached. After that point, the line will slope upwards, increasing by $2 for each additional movie watched.
The result will be a piecewise linear graph starting at $10 on the y-axis, remaining flat until the first movie, and then increasing linearly with a slope of 2 for every movie afterward.
Therefore, the best representation will have a horizontal line at $10 for the first movie, and after that, it will slope upwards in a straight line.