Question
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.
Number of Trees Purchased - Total Cost
1 - $60
2 - $100
3 - $150
4 - $190
5 - $230
Which best describes why the function is nonlinear?
A. The rate of change between 1 and 2 trees is different than the rate of change between 3 and 4 trees.
B. The rate of change between 3 and 4 trees is different than the rate of change between 4 and 5 trees.
C. The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
D. The rate of change between 1 and 2 trees is different than the rate of change between 4 and 5 trees.
Number of Trees Purchased - Total Cost
1 - $60
2 - $100
3 - $150
4 - $190
5 - $230
Which best describes why the function is nonlinear?
A. The rate of change between 1 and 2 trees is different than the rate of change between 3 and 4 trees.
B. The rate of change between 3 and 4 trees is different than the rate of change between 4 and 5 trees.
C. The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
D. The rate of change between 1 and 2 trees is different than the rate of change between 4 and 5 trees.
Answers
Answered by
GPT-4o mini
To determine the best option that describes why the function is nonlinear, we need to analyze the rate of change (the difference in total cost) between each pair of consecutive numbers of trees purchased.
Here's the breakdown of total costs:
- For 1 tree: $60
- For 2 trees: $100
- For 3 trees: $150
- For 4 trees: $190
- For 5 trees: $230
Now, let's find the change in cost between each pair:
1. Between 1 and 2 trees:
- Cost increases from $60 to $100.
- Change = $100 - $60 = $40
2. Between 2 and 3 trees:
- Cost increases from $100 to $150.
- Change = $150 - $100 = $50
3. Between 3 and 4 trees:
- Cost increases from $150 to $190.
- Change = $190 - $150 = $40
4. Between 4 and 5 trees:
- Cost increases from $190 to $230.
- Change = $230 - $190 = $40
Now, let's summarize the changes:
- 1 to 2 trees: $40
- 2 to 3 trees: $50
- 3 to 4 trees: $40
- 4 to 5 trees: $40
The rates of change are not constant; in particular, the rate of change between 2 and 3 trees is larger than the others. Specifically, this means there is a difference in rates of change which signals that the function is nonlinear.
With this analysis, we can say that:
C. The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
is the most accurate description of why the function is nonlinear. However, considering the choices, option A, which states that the rate of change between 1 and 2 trees is different than the rate of change between 3 and 4 trees, might also be applicable.
Ultimately, the most appropriate answer is:
**C. The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.**
Here's the breakdown of total costs:
- For 1 tree: $60
- For 2 trees: $100
- For 3 trees: $150
- For 4 trees: $190
- For 5 trees: $230
Now, let's find the change in cost between each pair:
1. Between 1 and 2 trees:
- Cost increases from $60 to $100.
- Change = $100 - $60 = $40
2. Between 2 and 3 trees:
- Cost increases from $100 to $150.
- Change = $150 - $100 = $50
3. Between 3 and 4 trees:
- Cost increases from $150 to $190.
- Change = $190 - $150 = $40
4. Between 4 and 5 trees:
- Cost increases from $190 to $230.
- Change = $230 - $190 = $40
Now, let's summarize the changes:
- 1 to 2 trees: $40
- 2 to 3 trees: $50
- 3 to 4 trees: $40
- 4 to 5 trees: $40
The rates of change are not constant; in particular, the rate of change between 2 and 3 trees is larger than the others. Specifically, this means there is a difference in rates of change which signals that the function is nonlinear.
With this analysis, we can say that:
C. The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
is the most accurate description of why the function is nonlinear. However, considering the choices, option A, which states that the rate of change between 1 and 2 trees is different than the rate of change between 3 and 4 trees, might also be applicable.
Ultimately, the most appropriate answer is:
**C. The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.**