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The given problem appears to ask for the initial population \( P \), using a growth model. Typically, this kind of problem uses an exponential growth formula, which is:

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

Where:
- \( A \) is the final amount (population after growth).
- \( P \) is the initial population (what we need to find).
- \( r \) is the growth rate per period (40% or 0.40).
- \( t \) is the time in years (11 years).
- \( A = 7,890,000 \) (final population).

Let me solve for \( P \) using this formula:

\[
P = \frac{A}{(1 + r)^t}
\]

Now let's calculate \( P \).The initial population \( P \) was approximately 194,836 people.

Would you like more details or clarifications? 

Here are five related questions:
1. How would the result change if the growth rate were 30% instead of 40%?
2. Can this formula be applied to any type of exponential growth, such as in economics?
3. What if the time period was 20 years? How would that affect the population?
4. How can we use logarithms to solve for \( t \) if the final population is known but not the time?
5. How would a decay rate affect this model, for example, in a population decline scenario?

**Tip**: When dealing with exponential growth, small changes in the rate \( r \) can result in large differences over time, especially for long durations.

Find the initial number of people. Given: A = 7,890,000, r = 40%, t = 11 years, P = ?

Learn how to calculate the initial population using the exponential growth model, with a given final population of 7,890,000, a growth rate of 40%, and a time period of 11 years. Suitable for students in Grades 9-12.

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