A club began with 3 members. Each month, each member brought one new member. Which function can be used to determine the number of members x months after the club began?



This problem describes a situation where the number of members in the club grows exponentially. Let's break it down:

- The club starts with 3 members.
- Each month, each existing member brings in 1 new member, which means the number of members doubles each month.

The general pattern for exponential growth can be modeled by the function:

\[
f(x) = P \times 2^x
\]

Where:
- \( P \) is the initial number of members (3 in this case),
- \( x \) is the number of months after the club began,
- \( 2^x \) represents the doubling effect every month.

Thus, the function that models the number of members after \( x \) months is:

\[
f(x) = 3 \times 2^x
\]

### Explanation:
- At month 0, there are 3 members: \( f(0) = 3 \times 2^0 = 3 \).
- At month 1, each member brings 1 new member, so the total number of members doubles: \( f(1) = 3 \times 2^1 = 6 \).
- At month 2, the number of members doubles again: \( f(2) = 3 \times 2^2 = 12 \), and so on.

Would you like more details on exponential growth or the next steps for solving specific values?

### Related Questions:
1. How many members will there be after 5 months?
2. How many members would the club have had after 3 months?
3. What if each member brought in 2 new members each month instead of 1?
4. How would the function change if the club started with 5 members?
5. What is the growth rate of the club's membership per month?

### Tip:
Always identify the pattern of growth in such problems (linear, exponential, etc.) to select the right mathematical model.

A club began with 3 members. Each month, each member brought one new member. Which function can be used to determine the number of members x months after the club began?

This problem explores how to model the number of club members over time using an exponential growth function. Given that each member recruits a new member every month, the function f(x) = 3 * 2^x shows how the club grows, starting with 3 members. Suitable for students in Grades 9-12.

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