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The problem asks for the correct exponential function that models the population of India after \( x \) years, given that:

- The initial population (in 2021) is 1.393 billion.
- The annual growth rate is 97% (which translates to 0.97 as a decimal).

The general form of an exponential growth function is:

\[
P(x) = P_0 \cdot (1 + r)^x
\]

Where:
- \( P_0 \) is the initial population (1.393 billion in this case).
- \( r \) is the rate of growth (0.97 or 97%).
- \( x \) is the number of years.

Applying these to the formula:

\[
P(x) = 1.393 \cdot (1 + 0.97)^x
\]

Looking at the answer choices:

- The correct choice is the second option: \( P(x) = 1.393 \cdot (1 + 0.97)^x \).

Explanation of why the other options are incorrect:
1. \( P(x) = 1.393 \cdot (1 + 0.97)^{2x} \) multiplies the exponent by 2, which is not correct for this scenario.
2. \( P(x) = 1.393 \cdot (1 + 0.97)^{x-1} \) incorrectly shifts the exponent by 1, suggesting a different starting point.
3. \( P(x) = 1.393 \cdot (1 + 0.97)^x + 0.5 \) adds an extra 0.5, which is unnecessary.

Let me know if you need any further clarification or details on exponential functions!

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Here are 5 questions related to this topic:
1. What would the population be after 10 years if this growth continues?
2. How would the model change if the growth rate was reduced to 50% annually?
3. Can you explain the difference between exponential and linear growth?
4. What does \( (1 + 0.97)^x \) mean in the context of this problem?
5. How would the equation look if the growth rate were negative?

**Tip:** Exponential growth occurs when the growth rate is proportional to the current value, making it faster over time.

The current population of India (2021) is 1.393 billion people, at an annual rate of increase of 97%. Which exponential function models the population, in billions of people, of India after x number of years?

Learn how to model India's population growth using an exponential function with a 97% annual growth rate. Starting with a population of 1.393 billion in 2021, find the correct function for future projections. Suitable for high school students learning about exponential growth.

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