The number of people that belong to a certain social website is 412 and growing at a rate of 5% every month.

How many members will there be in 9 months?

Enter your answer, rounded to the nearest whole number, in the box.

To solve this problem, we can use the formula for exponential growth:

\[
P(t) = P_0 \times (1 + r)^t
\]

Where:
- \( P(t) \) is the population after time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate per period, and
- \( t \) is the number of periods.

Given:
- \( P_0 = 412 \) (initial number of people),
- \( r = 5\% = 0.05 \),
- \( t = 9 \) months.

Plugging the values into the formula:

\[
P(9) = 412 \times (1 + 0.05)^9
\]

Now, let's calculate it.

\[
P(9) = 412 \times (1.05)^9 \approx 412 \times 1.5513 \approx 639.34
\]

Rounding to the nearest whole number, the number of members in 9 months will be approximately **639**.

Would you like any more details or have any questions?

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Here are some related questions you might find useful:
1. How would the answer change if the growth rate was 7%?
2. What would be the population after 12 months?
3. How long would it take for the population to double?
4. What is the monthly growth factor?
5. How would the formula change if the growth was compounded daily instead of monthly?
6. What if the initial population was 500 instead of 412?
7. How do we calculate continuous growth instead of discrete growth?
8. What are the implications of different compounding periods?

**Tip:** In exponential growth problems, small differences in the rate or time period can lead to significant changes in the outcome. Always ensure that your rate and time units match!

Learn how to calculate population growth using the exponential growth formula. Given an initial population of 412 growing at a rate of 5% every month, find out how many members there will be in 9 months. Follow a step-by-step solution with clear calculations and rounded results.

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