The initial population of a town is 3500​, and it grows with a doubling time of 10 years. What will the population be in 12 ​years?
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Part 1
What will the population be in 12 ​years?
  
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​(Round to the nearest whole number as​ needed.)

To find the population after 12 years given an initial population of 3500 and a doubling time of 10 years, we can use the formula for exponential growth:

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

where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( T \) is the doubling time,
- \( t \) is the time in years.

Plugging in the values:

- \( P_0 = 3500 \)
- \( T = 10 \) years
- \( t = 12 \) years

We can calculate:

\[
P(12) = 3500 \times 2^{\frac{12}{10}}
\]

Calculating \( \frac{12}{10} = 1.2 \):

\[
P(12) = 3500 \times 2^{1.2}
\]

Calculating \( 2^{1.2} \approx 2.297 \):

\[
P(12) \approx 3500 \times 2.297 \approx 8049.5
\]

Rounding to the nearest whole number, the population in 12 years will be approximately **8050**.

Would you like any further details or explanations? Here are some related questions you might consider:

1. How does the concept of doubling time apply to different populations?
2. What factors can affect the doubling time of a population?
3. How would the population change if the doubling time was shorter or longer?
4. What are the implications of exponential growth for resource management in a town?
5. How can we model population growth with different initial conditions? 

**Tip:** Always check the units of time when applying formulas for growth; they must be consistent!

The initial population of a town is 3500, and it grows with a doubling time of 10 years. What will the population be in 12 years?

Discover how to calculate the future population of a town starting with 3500 residents and doubling every 10 years. In 12 years, the population is projected to be approximately 8050. This explanation covers exponential growth concepts and related calculations.

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