*Question T5B10:
Which decibel value most closely represents a power decrease from 12 watts to 3 watts?*  

*Correct Answer is  C: -6 dB*  

### AI Response: (may contain errors)  

To determine the decibel value that represents a power decrease from 12 watts to 3 watts, we can use the formula for power in decibels (dB):

$$
P_{dB} = 10 \times \log_{10}\left(\frac{P_2}{P_1}\right)
$$

where:
- $P_1$ = initial power (12 watts)
- $P_2$ = final power (3 watts)

### Calculation:
1. Substitute the values into the formula:

$$
P_{dB} = 10 \times \log_{10}\left(\frac{3}{12}\right)
$$

2. Simplify the fraction:

$$
\frac{3}{12} = \frac{1}{4}
$$

3. Now calculate the logarithm:

$$
P_{dB} = 10 \times \log_{10}\left(\frac{1}{4}\right)
$$

4. Using the property of logarithms, we know that:

$$
\log_{10}\left(\frac{1}{4}\right) = -\log_{10}(4)
$$

5. The value of $\log_{10}(4)$ is approximately 0.602, so:

$$
P_{dB} = 10 \times (-0.602) \approx -6.02 \text{ dB}
$$

Thus, the closest decibel value representing the power decrease from 12 watts to 3 watts is approximately -6 dB.

### Explanation of Choices:
- **Correct Answer: -6 dB**
  - This value accurately reflects the calculated decrease in power from 12 watts to 3 watts.

- **Choice A: -1 dB**
  - This represents a very small decrease in power, which does not reflect the significant drop from 12 watts to 3 watts.

- **Choice B: -3 dB**
  - A -3 dB change corresponds to a power reduction to about half the original power (6 watts), which is still too high compared to the final power of 3 watts.

- **Choice D: -9 dB**
  - A -9 dB change would indicate a much larger decrease in power, approximately to 1.26 watts, which is not the case here.

### Summary:
- The correct answer is -6 dB because it accurately represents the power decrease from 12 watts to 3 watts.
- The other choices do not reflect the actual change in power based on the logarithmic scale used for decibels.