*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)  

In amateur radio, the S meter on a receiver is used to measure the strength of a received signal. The S meter is typically calibrated so that each S unit represents a 6 dB change in signal strength. 

To understand how much the power output must be raised to change the S meter reading from S8 to S9, we need to consider the relationship between power and decibels (dB). The formula to calculate the change in power in dB is:

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

where:
- $P_2$ is the final power level.
- $P_1$ is the initial power level.

Since each S unit represents a 6 dB change, increasing the S meter reading from S8 to S9 requires a 6 dB increase in power. 

To find the factor by which the power must be increased, we solve for $\frac{P_2}{P_1}$ when $\Delta \text{dB} = 6$:

$$
6 = 10 \log_{10} \left( \frac{P_2}{P_1} \right)
$$

Dividing both sides by 10:

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

To solve for $\frac{P_2}{P_1}$, we take the antilogarithm (base 10):

$$
\frac{P_2}{P_1} = 10^{0.6} \approx 4
$$

Therefore, the power output must be increased by approximately 4 times to change the S meter reading from S8 to S9.

**Explanation of Choices:**

- **A: Approximately 1.5 times**  
  This is incorrect because a 1.5 times increase corresponds to a much smaller dB change, not enough to increase by one S unit.

- **B: Approximately 2 times**  
  This is incorrect because a 2 times increase corresponds to a 3 dB change, which is only half of the required 6 dB change.

- **C: Approximately 4 times**  
  This is correct because a 4 times increase corresponds to a 6 dB change, which matches the requirement for increasing by one S unit.

- **D: Approximately 8 times**  
  This is incorrect because an 8 times increase corresponds to a 9 dB change, which is more than needed for a single S unit increase.