The value of t is inversely proportional to the value of w.If values of w increase by a factor of 5, what happen to the values of t?

Options

A. t increase by a factor of 5.
B. t increase by a factor of 2
C. t decrease by a factor of 2
D. t decrease by a factor of 5.

Answer

To solve the problem, we need to understand the relationship between the variables \( t \) and \( w \) given that \( t \) is inversely proportional to \( w \).

### Step-by-Step Solution:

1. **Understanding Inverse Proportionality**:
- When we say that \( t \) is inversely proportional to \( w \), we can express this relationship mathematically as:
\[ t \propto \frac{1}{w} \]
- This means that as \( w \) increases, \( t \) decreases, and vice versa.

2. **Setting Up the Equation**:
- We can write the relationship as:
\[ t = \frac{k}{w} \]
- Here, \( k \) is a constant of proportionality.

3. **Analyzing the Change in \( w \)**:
- According to the problem, the value of \( w \) increases by a factor of 5. This means:
\[ w' = 5w \]
- where \( w' \) is the new value of \( w \).

4. **Finding the New Value of \( t \)**:
- We can substitute \( w' \) into our equation for \( t \):
\[ t' = \frac{k}{w'} = \frac{k}{5w} \]
- This shows that the new value of \( t \) is:
\[ t' = \frac{1}{5} \cdot \frac{k}{w} = \frac{1}{5} t \]

5. **Conclusion**:
- Therefore, when the value of \( w \) increases by a factor of 5, the value of \( t \) decreases to \(\frac{1}{5}\) of its original value.

### Final Answer:
If the values of \( w \) increase by a factor of 5, the values of \( t \) decrease to \(\frac{1}{5}\) of their original value.

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