*Question G4D07:
How much must the power output of a transmitter be raised to change the S meter reading on a distant receiver from S8 to S9?*  

*Correct Answer is  C: Approximately 4 times*  

### AI Response: (may contain errors)  

To understand how much the power output of a transmitter must be raised to change the S meter reading from S8 to S9, we need to consider how the S meter works.

1. **Why the correct answer is correct:**
   - The S meter is a logarithmic scale that measures signal strength. Each S unit represents a specific increase in signal strength.
   - Moving from S8 to S9 represents a change of 1 S unit. In terms of power, an increase of 1 S unit corresponds to approximately a 6 dB increase in power.
   - To convert dB to a power ratio, we use the formula:
     $$ 
     P_{ratio} = 10^{(dB/10)} 
     $$
   - For a 6 dB increase:
     $$
     P_{ratio} = 10^{(6/10)} \approx 4
     $$
   - Therefore, to change the S meter reading from S8 to S9, the power output must be raised by a factor of approximately 4.

2. **Why the other choices are incorrect:**
   - **A: Approximately 1.5 times**: This would correspond to a much smaller increase in dB (about 1.76 dB), which is insufficient to change the S meter by 1 unit.
   - **B: Approximately 2 times**: This corresponds to a 3 dB increase, which is still not enough to achieve a full S unit change.
   - **D: Approximately 8 times**: This would correspond to a 9 dB increase, which is more than needed for a 1 S unit change.

3. **Useful formulas or rules of thumb:**
   - Each S unit increase (1 S point) is approximately equal to a 6 dB increase in power.
   - The power ratio for a dB increase can be calculated using:
     $$
     P_{ratio} = 10^{(dB/10)} 
     $$

In summary, to change the S meter reading from S8 to S9, you need to increase the transmitter power by a factor of approximately 4, which corresponds to a 6 dB increase.