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The question in the image states:

"One approximate formula for world population growth is \( T = 52.3 \ln 2 \), where \( T \) is the number of years for the population to double. According to this formula, how long does it take for the population to double?"

Let's solve this step by step:

1. The formula provided is:
   \[
   T = 52.3 \ln 2
   \]

2. The natural logarithm of 2, \(\ln 2\), is approximately 0.693.

3. Substitute \(\ln 2\) into the formula:
   \[
   T = 52.3 \times 0.693
   \]

4. Calculate the multiplication:
   \[
   T \approx 52.3 \times 0.693 \approx 36.2
   \]

So, the time it takes for the population to double is approximately **36 years**.

Would you like more details or have any questions?

Here are some related questions to explore further:
1. What is the significance of the natural logarithm in population growth models?
2. How does the doubling time change if the growth rate changes?
3. Can the formula be adapted for different growth rates or populations?
4. How does this model compare with other population growth models, like exponential or logistic growth?
5. What factors might cause deviations from this predicted doubling time in real-world populations?

**Tip:** Understanding natural logarithms can be crucial in growth-related formulas, as they help simplify complex exponential relationships into linear ones.

One approximate formula for world population growth is T = 52.3 ln(2), where T is the number of years for the population to double. According to this formula, how long does it take for the population to double?

Learn how to calculate the doubling time of the world population using the formula T = 52.3 ln(2). This step-by-step guide covers key mathematical concepts including logarithms and population growth models. Suitable for high school students studying exponential growth and natural logarithms.

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