Math Problem Statement
Solution
To determine the correct answer for this problem, let's break down the function and analyze its domain and range.
Given Information
- Function:
- Context: represents the number of weeks since Jackie’s birthday, and is the amount of money remaining.
- Initial amount: $250
- Spending: $10 each week
Analyzing the Domain
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Starting Point: At , Jackie has $250 (initial amount).
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End Condition: Jackie spends $10 each week. When she runs out of money, will be 0.
Setting :
So, Jackie will have money from to weeks.
Therefore, the domain for this situation is , where is an integer (since we are counting weeks).
Analyzing the Range
-
Maximum Value: At , .
-
Minimum Value: At , .
Therefore, the range of is .
Answer Choice
The correct answer matches this domain and range.
Looking at the options:
- Option C matches our analysis:**
- Domain: ,
- Range:
Thus, the correct answer is Option C.
Would you like a detailed explanation of each step?
Here are 5 related questions that could deepen your understanding:
- How would the domain and range change if Jackie spent $5 per week instead of $10?
- What would happen to the function if the initial amount was increased to $300?
- How would you determine the domain and range if Jackie spent a different amount each week?
- Can you create a similar function if Jackie deposited $10 each week instead of spending it?
- What does the graph of look like over the domain ?
Tip: Always identify the initial condition and rate of change to help determine the domain and range in word problems like these.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Domain and Range
Formulas
A(t) = 250 - 10t
Theorems
-
Suitable Grade Level
Grades 8-10
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