Math Problem Statement
The cost of a particular private school begins with a one-time initiation fee of $20002000, plus annual tuition of $6 comma 0006,000. This situation can be modeled by a linear function. Identify the independent and dependent variables. Draw a graph of the function, then use the graph to find the cost to attend this school for 44 years. Is a linear model reasonable for this situation? Question content area bottom left Part 1 The number of years is the ▼ independent dependent variable. The cost is the ▼ independent dependent variable.
Solution
The graph shows the total cost of attending the private school over time. For 4 years of attendance, the total cost is $26,000.
Is a linear model reasonable?
Yes, a linear model is reasonable in this case because the cost increases by a fixed amount ($6,000) each year, which is characteristic of a linear relationship. The one-time initiation fee adds a constant to the cost, but it doesn't affect the linearity of the model over time.
Would you like more details on this or have any other questions? Here are 5 related questions you might find helpful:
- How would the function change if the initiation fee were higher or lower?
- What if there were a yearly increase in tuition of a fixed percentage?
- How would the total cost change if the student attended for 10 years?
- How can you calculate the break-even point between two schools with different tuition costs?
- How would the graph change if there were a yearly discount applied after 5 years?
Tip: Linear models are best suited for situations where changes are consistent over time, such as a constant yearly fee or rate.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Graphing
Variables
Formulas
Total Cost = 6000 * Years + 2000
Theorems
Linear Relationship Theorem
Suitable Grade Level
Grades 6-8