Math Problem Statement
Solution
The table shows a set of values for and , where could represent time (e.g., days, months) and represents some quantity that changes over time.
The data in the table is:
0 | 8 |
1 | 9.5 |
2 | 11 |
3 | 12.5 |
Let's break down the given options and analyze which one matches this dataThe table shows a set of values for and , where could represent time (e.g., days, months) and represents some quantity that changes over time.
The data in the table is:
0 | 8 |
1 | 9.5 |
2 | 11 |
3 | 12.5 |
Let's break down the given options and analyze which one matches this
Option A:
"Robbie has $8 in his account and spends $1.50 each day for the next 3 days."
- At (day 0), Robbie has $8.
- Each day, he spends $1.50, so after 1 day (when ), he would have , and this does not match the value of in the table. This option does not fit.
Option B:
"Zach sells t-shirts for $9.50 each."
- This doesn't involve any specific rate of change over time or relate to the given and data. So, this option does not match.
Option C:
"A newborn weighs 8 pounds at birth and gains 1.5 pounds each month for the next 3 months."
- At (birth), the weight is 8 pounds.
- After 1 month (), the baby gains 1.5 pounds, making the weight pounds.
- After 2 months (), the baby weighs pounds.
- After 3 months (), the baby weighs pounds.
This matches perfectly with the data in the table.
Option D:
"Riley earns $8 an hour lifeguarding, plus $1.50 for any pool memberships she sells."
- This suggests a linear relationship, but the numbers do not correspond to the data in the table, as Riley's earnings don't match the values of based on the table’s .
Conclusion:
The situation that best matches the data in the table is Option C, where the newborn weighs 8 pounds at birth and gains 1.5 pounds each month for the next 3 months.
Would you like more details on this solution or have any further questions?
Here are 5 related questions to expand on this problem:
- How would the equation of this linear relationship between and be written?
- If the newborn continued gaining weight at the same rate, what would its weight be at 6 months?
- How can we represent the situation in a graph and what would the slope represent?
- How can you check whether a situation represents a linear function?
- How does the rate of change affect the interpretation of real-world problems?
Tip: In problems involving linear relationships, always check for a constant rate of change by comparing differences in values as increases.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Relationships
Rate of Change
Formulas
y = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 6-8