The initial population of a town is 2900​, and it grows with a doubling time of 10 years. What will the population be in 12 ​years?

To calculate the population of the town after 12 years, we can use the formula for exponential growth:

\[
P(t) = P_0 \times 2^{\frac{t}{T}}
\]

where:
- \( P(t) \) is the population after time \( t \).
- \( P_0 \) is the initial population.
- \( t \) is the time elapsed.
- \( T \) is the doubling time.

Given:
- \( P_0 = 2900 \)
- \( t = 12 \) years
- \( T = 10 \) years

Substituting the values into the formula:

\[
P(12) = 2900 \times 2^{\frac{12}{10}} = 2900 \times 2^{1.2}
\]

Now, calculate \( 2^{1.2} \):

\[
2^{1.2} \approx 2.297
\]

Thus,

\[
P(12) \approx 2900 \times 2.297 \approx 6661.3
\]

The population after 12 years will be approximately **6661**.

Would you like more details or have any questions? Here are some related questions:

1. How does changing the doubling time affect the future population?
2. What would the population be after 20 years?
3. How would the calculation change if the growth rate were 5% per year instead of doubling every 10 years?
4. Can this model be applied to populations that decline over time?
5. How does exponential growth compare to linear growth in population studies?

**Tip:** In exponential growth, small changes in time or growth rate can lead to significant differences in the population over longer periods.

Explore how to calculate the population growth of a town using exponential growth. Given an initial population of 2900 and a doubling time of 10 years, learn how to predict the population after 12 years. Includes step-by-step calculation and explanation.

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