4. At Gunterville College, tuition rates for in-state residents were $92 per credit for the first 10 credits, $35 per credit for credits 11-18, and for over 18 credits the rate is $74 per credit. Write a piecewise defined function for the total tuition, T, at Gunterville College as a function of the number of credits taken, c. Be sure to consider a reasonable domain and range.

how much for 17 credits

We are given a scenario where the tuition rates at Gunterville College are based on the number of credits taken, with different rates for different ranges of credits.

### Tuition rates:
1. **$92 per credit** for the first 10 credits.
2. **$35 per credit** for credits 11 to 18.
3. **$74 per credit** for any credits over 18.

### Let's define a piecewise function for the total tuition $ T(c) $ in terms of the number of credits $ c $:

\[
T(c) =
\begin{cases} 
92c & \text{if } 0 \leq c \leq 10, \\
920 + 35(c - 10) & \text{if } 10 < c \leq 18, \\
920 + 35(8) + 74(c - 18) & \text{if } c > 18.
\end{cases}
\]

#### Explanation:
- If $ c \leq 10 $, the total cost is simply $ 92c $.
- If $ 10 < c \leq 18 $, the first 10 credits cost $ 92 \times 10 = 920 $ dollars. For each additional credit beyond 10, the cost is $ 35 $ dollars.
- If $ c > 18 $, the first 10 credits cost $ 920 $, the next 8 credits (from 11 to 18) cost $ 35 \times 8 = 280 $, and any credits beyond 18 are charged at $ 74 $ dollars per credit.

### For 17 credits:
Since 17 credits fall in the range $ 10 < c \leq 18 $, we use the second part of the piecewise function:

\[
T(17) = 920 + 35(17 - 10) = 920 + 35(7) = 920 + 245 = 1165.
\]

So, the total tuition for 17 credits is **$1,165**.

Would you like more details on how I derived this piecewise function?

### Related Questions:
1. How much would the tuition be for 10 credits?
2. What is the total tuition for 19 credits?
3. How would the function change if the rates for credits over 18 were different?
4. What is the maximum tuition cost if a student takes 18 credits?
5. How would you define the domain and range for this piecewise function?

**Tip:** Piecewise functions are used to model situations where a rule or relationship changes depending on the input value.

At Gunterville College, tuition rates for in-state residents were $92 per credit for the first 10 credits, $35 per credit for credits 11-18, and for over 18 credits the rate is $74 per credit. Write a piecewise defined function for the total tuition, T, at Gunterville College as a function of the number of credits taken, c. How much for 17 credits?

Learn how to calculate the total tuition at Gunterville College using a piecewise function. This example shows the rates per credit for different ranges, and solves the tuition for 17 credits, costing $1,165. Suitable for high school students studying functions and real-life applications of piecewise functions.

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