*Question T5B11:
Which decibel value represents a power increase from 20 watts to 200 watts?*  

*Correct Answer is  A: 10 dB*  

### AI Response: (may contain errors)  

To determine the decibel (dB) value representing a power increase from 20 watts to 200 watts, we can use the formula for power in decibels:

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

where:
- $P_1$ = initial power (20 watts)
- $P_2$ = final power (200 watts)

### Calculation:
1. Substitute the values into the formula:
   $$
   dB = 10 \times \log_{10}\left(\frac{200}{20}\right)
   $$
2. Simplify the fraction:
   $$
   \frac{200}{20} = 10
   $$
3. Now calculate the logarithm:
   $$
   \log_{10}(10) = 1
   $$
4. Finally, multiply by 10:
   $$
   dB = 10 \times 1 = 10 \text{ dB}
   $$

### Explanation of the Correct Answer:
- The correct answer is **10 dB** because the power increased by a factor of 10 (from 20 watts to 200 watts), which corresponds to a 10 dB increase.

### Why the Other Choices are Incorrect:
- **12 dB**: This would imply a power increase by a factor of approximately 16 (since $10 \times \log_{10}(16) \approx 12$), which is not the case here.
- **18 dB**: This would imply a power increase by a factor of approximately 63 (since $10 \times \log_{10}(63) \approx 18$), which is also incorrect.
- **28 dB**: This would imply a power increase by a factor of approximately 630 (since $10 \times \log_{10}(630) \approx 28$), which is far too high for the given values.

### Summary:
- The increase from 20 watts to 200 watts is a 10-fold increase, resulting in a 10 dB increase in power. The other choices represent incorrect factors of power increase based on the logarithmic scale used in decibels.