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?
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Part 1
The number of years is the 
▼ 
independent
dependent
 variable. The cost is the 
▼ 
independent
dependent
 variable.

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:

1. How would the function change if the initiation fee were higher or lower?
2. What if there were a yearly increase in tuition of a fixed percentage?
3. How would the total cost change if the student attended for 10 years?
4. How can you calculate the break-even point between two schools with different tuition costs?
5. 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.

The cost of a particular private school begins with a​ one-time initiation fee of ​$2000, plus annual tuition of ​$6,000. 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 4 years. Is a linear model reasonable for this situation?

Explore how to use a linear function to model the total cost of attending a private school. This problem involves calculating costs based on a one-time fee of $2000 and an annual tuition of $6,000. Learn how to graph the function and use it to determine the cost for 4 years. Suitable for students in Grades 6-8.

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