Question
The table shows the cost, y, when a bike is rented for x number of hours.
Bike Rentals
Hour, x Cost, y
0 4
1 5.5
3 8.5
5 11.5
7 14.5
What is the meaning of the initial value and the rate of change for the situation?
Responses
A The initial base charge to rent a bike is $1.50 and the additional hourly charge for the bike rental is $4.00 per hour.The initial base charge to rent a bike is $1.50 and the additional hourly charge for the bike rental is $4.00 per hour.
B The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $3.00 per hour.The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $3.00 per hour.
C The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour.The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour.
D The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $2.00 per hour.
Bike Rentals
Hour, x Cost, y
0 4
1 5.5
3 8.5
5 11.5
7 14.5
What is the meaning of the initial value and the rate of change for the situation?
Responses
A The initial base charge to rent a bike is $1.50 and the additional hourly charge for the bike rental is $4.00 per hour.The initial base charge to rent a bike is $1.50 and the additional hourly charge for the bike rental is $4.00 per hour.
B The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $3.00 per hour.The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $3.00 per hour.
C The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour.The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour.
D The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $2.00 per hour.
Answers
Answered by
QuestionHelper123
C
Answered by
GPT-4o mini
To analyze the data provided in the table, let's identify the initial value and the rate of change.
The initial value is the cost when no hours are rented (x = 0), which is $4. This represents the base charge for renting the bike.
Next, we need to determine the rate of change, which is the amount the cost increases for each additional hour rented. To find this, we can look at the costs at consecutive hours.
1. From 0 to 1 hour:
Cost changes from $4 to $5.5. Increase: $5.5 - $4 = $1.5 for 1 hour.
2. From 1 to 3 hours:
Cost changes from $5.5 to $8.5. Increase: $8.5 - $5.5 = $3 for 2 hours.
Average increase per hour: $3 / 2 = $1.5 per hour.
3. From 3 to 5 hours:
Cost changes from $8.5 to $11.5. Increase: $11.5 - $8.5 = $3 for 2 hours.
Average increase per hour: $3 / 2 = $1.5 per hour.
4. From 5 to 7 hours:
Cost changes from $11.5 to $14.5. Increase: $14.5 - $11.5 = $3 for 2 hours.
Average increase per hour: $3 / 2 = $1.5 per hour.
Consistently, we see that the cost increases by $1.50 for each hour rented after the initial fee of $4.
Now, comparing our findings with the given options:
- The initial charge is **$4.00**.
- The additional cost per hour is **$1.50**.
Thus, the correct answer is:
**C** The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour.
The initial value is the cost when no hours are rented (x = 0), which is $4. This represents the base charge for renting the bike.
Next, we need to determine the rate of change, which is the amount the cost increases for each additional hour rented. To find this, we can look at the costs at consecutive hours.
1. From 0 to 1 hour:
Cost changes from $4 to $5.5. Increase: $5.5 - $4 = $1.5 for 1 hour.
2. From 1 to 3 hours:
Cost changes from $5.5 to $8.5. Increase: $8.5 - $5.5 = $3 for 2 hours.
Average increase per hour: $3 / 2 = $1.5 per hour.
3. From 3 to 5 hours:
Cost changes from $8.5 to $11.5. Increase: $11.5 - $8.5 = $3 for 2 hours.
Average increase per hour: $3 / 2 = $1.5 per hour.
4. From 5 to 7 hours:
Cost changes from $11.5 to $14.5. Increase: $14.5 - $11.5 = $3 for 2 hours.
Average increase per hour: $3 / 2 = $1.5 per hour.
Consistently, we see that the cost increases by $1.50 for each hour rented after the initial fee of $4.
Now, comparing our findings with the given options:
- The initial charge is **$4.00**.
- The additional cost per hour is **$1.50**.
Thus, the correct answer is:
**C** The initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour.
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