https://file.aiquickdraw.com/mathbot/file/17266317037140nd58ohx.jpg

Let's solve the problem step by step by analyzing the table provided:

We are given that \( C = f(n) \), which represents the total cost for a carpenter to build \( n \) wooden chairs. The table shows the values of \( C(n) \) for different values of \( n \).

| \( n \)   | 0    | 15   | 30   | 45   | 60   | 75   |
|-----------|------|------|------|------|------|------|
| \( C(n) \) | 4000 | 5000 | 5900 | 6500 | 7000 | 7400 |

### Now let's evaluate the given expressions:

(a) \( f(15) \):  
From the table, when \( n = 15 \), \( C(n) = 5000 \).  
So, \( f(15) = 5000 \).

(b) \( f(x) \) when \( x = 45 \):  
From the table, when \( n = 45 \), \( C(n) = 6500 \).  
So, \( f(45) = 6500 \).

(c) \( z \) when \( f(z) = 5900 \):  
From the table, when \( f(n) = 5900 \), \( n = 30 \).  
So, \( z = 30 \).

(d) \( f(0) \):  
From the table, when \( n = 0 \), \( C(n) = 4000 \).  
So, \( f(0) = 4000 \).

### Answers:
- (a) \( f(15) = 5000 \)
- (b) \( f(45) = 6500 \)
- (c) \( z = 30 \)
- (d) \( f(0) = 4000 \)

Would you like more details or have any questions? 

Here are some related questions you can explore:
1. How would you interpolate values for \( f(n) \) if \( n \) is not listed in the table?
2. What if \( f(n) \) followed a linear pattern, could you find the equation for \( f(n) \)?
3. How can you use this table to predict the cost for \( n = 90 \)?
4. How would you graph the function \( f(n) \) based on the table?
5. Can you estimate the rate of increase in cost as more chairs are built?

**Tip:** To better understand data trends, try graphing the function values to see the pattern.

The table below gives the total cost, C = f(n), for a carpenter to build n wooden chairs. Evaluate the expressions based on the given data.

Explore how to evaluate the cost function f(n) for a carpenter building wooden chairs using the provided table. Learn how to find values such as f(15), f(45), and solve for z when f(z) = 5900. Suitable for Grades 7-9.

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