Missing term in the following table is `{:(x " " : 0 , 1 , 2 , 3 ,4) , ( y = f(x) : 1,3,9, ? , 81):}`

Options

A. 27
B. 30
C. 31
D. 34

Explanation

To find the missing term in the table, we will analyze the values given and derive a relationship between them. The table provides the following data:

- \( x: 0, 1, 2, 3, 4 \)
- \( y = f(x): 1, 3, 9, ?, 81 \)

### Step-by-Step Solution

1. **Identify the Values**:
We have the following pairs:
- \( f(0) = 1 \)
- \( f(1) = 3 \)
- \( f(2) = 9 \)
- \( f(3) = ? \)
- \( f(4) = 81 \)

2. **Look for a Pattern**:
Let's observe the relationship between the \( x \) values and the corresponding \( f(x) \) values:
- \( f(0) = 1 = 3^0 \)
- \( f(1) = 3 = 3^1 \)
- \( f(2) = 9 = 3^2 \)
- \( f(4) = 81 = 3^4 \)

This suggests that \( f(x) = 3^x \).

3. **Calculate \( f(3) \)**:
Using the identified pattern, we can calculate \( f(3) \):
\[ f(3) = 3^3 = 27 \]

4. **Conclusion**:
The missing term in the table, which is \( f(3) \), is \( 27 \).

### Final Answer:
The missing term is \( 27 \).

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