Question
a movie streaming service charges $10 up front and $2 for each movie is thereafter. Which graph best represents the cost of watching movies over time?
A. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 20 in increments of 2 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Six unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 6 comma 7 right parenthesis, left parenthesis 8 comma 6 right parenthesis, and left parenthesis 10 comma 5 right parenthesis. A solid arrow passes through these points.
B. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 12 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Three unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
C. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Four unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 1 comma 3 right parenthesis, left parenthesis 2 comma 4 right parenthesis, and left parenthesis 3 comma 5 right parenthesis. A solid arrow passes through these points.
D. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Five unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 14 right parenthesis, left parenthesis 3 comma 16 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
A. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 20 in increments of 2 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Six unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 6 comma 7 right parenthesis, left parenthesis 8 comma 6 right parenthesis, and left parenthesis 10 comma 5 right parenthesis. A solid arrow passes through these points.
B. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 12 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Three unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
C. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Four unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 1 comma 3 right parenthesis, left parenthesis 2 comma 4 right parenthesis, and left parenthesis 3 comma 5 right parenthesis. A solid arrow passes through these points.
D. A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Five unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 14 right parenthesis, left parenthesis 3 comma 16 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
Answers
GPT-4o mini
To determine which graph best represents the cost of watching movies over time, we need to analyze the pricing structure of the movie streaming service:
1. **Upfront Cost**: $10 (this is the cost for the first movie)
2. **Cost per Movie Thereafter**: $2 per movie after the first one.
The total cost for watching `n` movies can be modeled by the following equation:
- If `n = 0` (no movies), the cost is $10.
- If `n = 1` (just the first movie), the cost is $10.
- If `n >= 2`, the total cost is given by:
\[
\text{Total Cost} = 10 + 2(n - 1) = 10 + 2n - 2 = 2n + 8
\]
This means:
- Total cost when 0 movies are watched: $10
- Total cost when 1 movie is watched: $10
- Total cost when 2 movies are watched: $12
- Total cost when 3 movies are watched: $14
- Total cost when 4 movies are watched: $16
- Total cost when 5 movies are watched: $18
Now let’s analyze the answer options:
- **Option A**: Contains points that do not match the cost structure we derived.
- **Option B**: Only has three points and the y-values don’t follow the derived costs.
- **Option C**: Also has incorrect points that don’t match the price structure.
- **Option D**: Matches our derived costs:
- (0, 10)
- (1, 10)
- (2, 12)
- (3, 14)
- (4, 16)
- (5, 18)
Based on this analysis, the correct graph that represents the cost of watching movies over time is:
**Option D**.
1. **Upfront Cost**: $10 (this is the cost for the first movie)
2. **Cost per Movie Thereafter**: $2 per movie after the first one.
The total cost for watching `n` movies can be modeled by the following equation:
- If `n = 0` (no movies), the cost is $10.
- If `n = 1` (just the first movie), the cost is $10.
- If `n >= 2`, the total cost is given by:
\[
\text{Total Cost} = 10 + 2(n - 1) = 10 + 2n - 2 = 2n + 8
\]
This means:
- Total cost when 0 movies are watched: $10
- Total cost when 1 movie is watched: $10
- Total cost when 2 movies are watched: $12
- Total cost when 3 movies are watched: $14
- Total cost when 4 movies are watched: $16
- Total cost when 5 movies are watched: $18
Now let’s analyze the answer options:
- **Option A**: Contains points that do not match the cost structure we derived.
- **Option B**: Only has three points and the y-values don’t follow the derived costs.
- **Option C**: Also has incorrect points that don’t match the price structure.
- **Option D**: Matches our derived costs:
- (0, 10)
- (1, 10)
- (2, 12)
- (3, 14)
- (4, 16)
- (5, 18)
Based on this analysis, the correct graph that represents the cost of watching movies over time is:
**Option D**.