Question
A bicycle rental company charges $3 up front and $1 for every 15 minutes thereafter. Which graph best represents the cost of the bicycle rental over time?(1 point)
Responses
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 9 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 3 right parenthesis, left parenthesis 1 comma 4 right parenthesis, left parenthesis 2 comma 5 right parenthesis, left parenthesis 3 comma 6 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 9 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 3 right parenthesis, left parenthesis 1 comma 4 right parenthesis, left parenthesis 2 comma 5 right parenthesis, left parenthesis 3 comma 6 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 35 in increments of 5 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 10 comma 5 right parenthesis, left parenthesis 15 comma 6 right parenthesis, left parenthesis 20 comma 7 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 35 in increments of 5 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 10 comma 5 right parenthesis, left parenthesis 15 comma 6 right parenthesis, left parenthesis 20 comma 7 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 90 in increments of 15 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 15 comma 4 right parenthesis, left parenthesis 30 comma 5 right parenthesis, left parenthesis 45 comma 6 right parenthesis, left parenthesis 60 comma 7 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 90 in increments of 15 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 15 comma 4 right parenthesis, left parenthesis 30 comma 5 right parenthesis, left parenthesis 45 comma 6 right parenthesis, left parenthesis 60 comma 7 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 90 in increments of 15 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Three unlabeled points are plotted as follows: left parenthesis 15 comma 0 right parenthesis, left parenthesis 30 comma 3 right parenthesis, left parenthesis 45 comma 6 right parenthesis. A solid arrow passes through these points.
Responses
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 9 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 3 right parenthesis, left parenthesis 1 comma 4 right parenthesis, left parenthesis 2 comma 5 right parenthesis, left parenthesis 3 comma 6 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 9 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 3 right parenthesis, left parenthesis 1 comma 4 right parenthesis, left parenthesis 2 comma 5 right parenthesis, left parenthesis 3 comma 6 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 35 in increments of 5 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 10 comma 5 right parenthesis, left parenthesis 15 comma 6 right parenthesis, left parenthesis 20 comma 7 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 35 in increments of 5 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 10 comma 5 right parenthesis, left parenthesis 15 comma 6 right parenthesis, left parenthesis 20 comma 7 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 90 in increments of 15 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 15 comma 4 right parenthesis, left parenthesis 30 comma 5 right parenthesis, left parenthesis 45 comma 6 right parenthesis, left parenthesis 60 comma 7 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 90 in increments of 15 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Five unlabeled points are plotted as follows: left parenthesis 0 comma 3 right parenthesis, left parenthesis 15 comma 4 right parenthesis, left parenthesis 30 comma 5 right parenthesis, left parenthesis 45 comma 6 right parenthesis, left parenthesis 60 comma 7 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 90 in increments of 15 and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Three unlabeled points are plotted as follows: left parenthesis 15 comma 0 right parenthesis, left parenthesis 30 comma 3 right parenthesis, left parenthesis 45 comma 6 right parenthesis. A solid arrow passes through these points.
Answers
GPT-4o mini
To determine which graph best represents the cost of the bicycle rental over time, we need to analyze the pricing structure:
1. The upfront cost is $3.
2. After the first 15 minutes, there is an additional charge of $1 for every 15 minutes.
Let's break down the cost based on different time intervals:
- For 0 minutes, the cost is $3.
- For 15 minutes (0 to 15): Cost = $3 + $1 * 1 = $4.
- For 30 minutes (15 to 30): Cost = $3 + $1 * 2 = $5.
- For 45 minutes (30 to 45): Cost = $3 + $1 * 3 = $6.
- For 60 minutes (45 to 60): Cost = $3 + $1 * 4 = $7.
- And so on...
Now, let's evaluate the provided graphs:
- **First Graph:** Points: (0, 3), (1, 4), (2, 5), (3, 6). This graph shows a continuous increase in cost even for very short time intervals which is incorrect because costs should only increase at 15-minute intervals, not continuously every minute.
- **Second Graph:** Points: (0, 3), (5, 4), (10, 5), (15, 6), (20, 7). This graph also shows non-discrete increases, which is not aligned with our pricing model.
- **Third Graph:** Points: (0, 3), (15, 4), (30, 5), (45, 6), (60, 7). This graph correctly depicts the price increase at every 15-minute increment, adhering to the pricing rules.
- **Fourth Graph:** Points: (15, 0), (30, 3), (45, 6). This graph incorrectly begins at (15, 0) which does not reflect the upfront cost added for the rental.
Thus, **the third graph** accurately represents the cost structure of the bike rental with points correlated to the pricing system at specific time increments.
1. The upfront cost is $3.
2. After the first 15 minutes, there is an additional charge of $1 for every 15 minutes.
Let's break down the cost based on different time intervals:
- For 0 minutes, the cost is $3.
- For 15 minutes (0 to 15): Cost = $3 + $1 * 1 = $4.
- For 30 minutes (15 to 30): Cost = $3 + $1 * 2 = $5.
- For 45 minutes (30 to 45): Cost = $3 + $1 * 3 = $6.
- For 60 minutes (45 to 60): Cost = $3 + $1 * 4 = $7.
- And so on...
Now, let's evaluate the provided graphs:
- **First Graph:** Points: (0, 3), (1, 4), (2, 5), (3, 6). This graph shows a continuous increase in cost even for very short time intervals which is incorrect because costs should only increase at 15-minute intervals, not continuously every minute.
- **Second Graph:** Points: (0, 3), (5, 4), (10, 5), (15, 6), (20, 7). This graph also shows non-discrete increases, which is not aligned with our pricing model.
- **Third Graph:** Points: (0, 3), (15, 4), (30, 5), (45, 6), (60, 7). This graph correctly depicts the price increase at every 15-minute increment, adhering to the pricing rules.
- **Fourth Graph:** Points: (15, 0), (30, 3), (45, 6). This graph incorrectly begins at (15, 0) which does not reflect the upfront cost added for the rental.
Thus, **the third graph** accurately represents the cost structure of the bike rental with points correlated to the pricing system at specific time increments.