What is the rate of change in the size of Vanessa's client base between months $$3 and $$4?

To find the rate of change in the size of Vanessa's client base between months 3 and 4, follow these steps:

1. ### Break Down the Problem

You need to identify the size of the client base at the end of month 3 and month 4. The rate of change can then be calculated using the formula:

$\text{Rate of Change} = \frac{\text{Size at Month 4} - \text{Size at Month 3}}{\text{Month 4} - \text{Month 3}}$

2. ### Relevant Concepts

The rate of change formula represents the average rate of change of a function over a specific interval. In this case, it compares the sizes of the client base over the interval from month 3 to month 4.

3. ### Analysis and Detail

1. Let $C_3$ be the size of the client base at the end of month 3.
2. Let $C_4$ be the size of the client base at the end of month 4.
3. Calculate the difference $C_4 - C_3$.
4. Since the time interval between month 3 and month 4 is 1 month ($4 - 3 = 1$), the rate of change simplifies to:

$\text{Rate of Change} = C_4 - C_3$

4. ### Verify and Summarize

Confirm the values of $C_3$ and $C_4$ through the given data if available. Perform the subtraction to find the rate of change.

Final Answer

The rate of change in the size of Vanessa's client base between months 3 and 4 is $C_4 - C_3$ (where $C_4$ and $C_3$ are the respective client base sizes at the end of month 4 and month 3). Please provide the client base sizes to compute the exact rate of change.