Question
A newborn kitten weighs 3 ounces at birth. After four weeks, it weighs 13 ounces. Which of the following is true?
A.
The kitten's age and weight are not in a proportional relationship because the difference in the weight of the kitten after four weeks is 10 ounces.
B.
The kitten's age and weight are not in a proportional relationship because the kitten does not weigh zero ounces at birth.
C.
The kitten's age and weight are not in a proportional relationship because the weight of the kitten increases by 2.5 ounces every week.
D.
The kitten's age and weight are not in a proportional relationship because the weight of the kitten increases over time.
A.
The kitten's age and weight are not in a proportional relationship because the difference in the weight of the kitten after four weeks is 10 ounces.
B.
The kitten's age and weight are not in a proportional relationship because the kitten does not weigh zero ounces at birth.
C.
The kitten's age and weight are not in a proportional relationship because the weight of the kitten increases by 2.5 ounces every week.
D.
The kitten's age and weight are not in a proportional relationship because the weight of the kitten increases over time.
Answers
GPT-4o mini
The correct answer is **C**.
To understand why, we first clarify what it means for two quantities to be in a proportional relationship. Two quantities \( x \) and \( y \) are proportional if they maintain a constant ratio (or can be expressed as \( y = kx \) for some constant \( k \)).
In this case, the kitten's weight at birth is 3 ounces, and after 4 weeks, it is 13 ounces. Let's look at the weekly weight gain:
- Initially, at birth (week 0): 3 ounces
- After 1 week: 4 ounces (not given, but let's assume some increase)
- After 2 weeks: 5 ounces (again, hypothetically increasing)
- After 3 weeks: around 8 ounces (this isn't specified)
- After 4 weeks: 13 ounces
If we divide the total weight increase by the number of weeks (10 ounces over 4 weeks), that gives an average increase of \( 10 \text{ ounces} / 4 \text{ weeks} = 2.5 \text{ ounces/week} \). This means the weight gain per week is consistent.
However, for a relationship to be proportional, the ratios must remain constant. In this case, since the kitten weighs 3 ounces at birth and it weighs 13 ounces after four weeks, the ratio of weight to age is not constant.
Therefore, option C is true because the kitten's weight gain isn't proportional; it increases steadily, not maintaining a constant proportional relationship.
To understand why, we first clarify what it means for two quantities to be in a proportional relationship. Two quantities \( x \) and \( y \) are proportional if they maintain a constant ratio (or can be expressed as \( y = kx \) for some constant \( k \)).
In this case, the kitten's weight at birth is 3 ounces, and after 4 weeks, it is 13 ounces. Let's look at the weekly weight gain:
- Initially, at birth (week 0): 3 ounces
- After 1 week: 4 ounces (not given, but let's assume some increase)
- After 2 weeks: 5 ounces (again, hypothetically increasing)
- After 3 weeks: around 8 ounces (this isn't specified)
- After 4 weeks: 13 ounces
If we divide the total weight increase by the number of weeks (10 ounces over 4 weeks), that gives an average increase of \( 10 \text{ ounces} / 4 \text{ weeks} = 2.5 \text{ ounces/week} \). This means the weight gain per week is consistent.
However, for a relationship to be proportional, the ratios must remain constant. In this case, since the kitten weighs 3 ounces at birth and it weighs 13 ounces after four weeks, the ratio of weight to age is not constant.
Therefore, option C is true because the kitten's weight gain isn't proportional; it increases steadily, not maintaining a constant proportional relationship.