A barangay has 1,000 individuals and its population doubles every 60 years. Give an 
exponential model for the barangay. What is the barangay’s population in 10 years?

The problem describes exponential population growth, where the population doubles every 60 years. An exponential growth model can be expressed as:

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

Where:
- \( P(t) \) is the population at time \( t \) years,
- \( P_0 \) is the initial population (1,000 individuals),
- \( T \) is the doubling time (60 years),
- \( t \) is the time in years.

Using this formula:
- \( P_0 = 1,000 \)
- \( T = 60 \)

The exponential model becomes:

\[
P(t) = 1,000 \cdot 2^{\frac{t}{60}}
\]

Now, to find the population in 10 years (\( t = 10 \)):

\[
P(10) = 1,000 \cdot 2^{\frac{10}{60}} = 1,000 \cdot 2^{\frac{1}{6}}
\]

We can now calculate this.

\[
P(10) \approx 1,000 \cdot 1.122
\]

\[
P(10) \approx 1,122
\]

So, the barangay’s population in 10 years will be approximately **1,122 individuals**.

Would you like more details on the steps? 

Here are 5 related questions:
1. What happens to the population after 30 years?
2. How do we interpret the doubling time in exponential growth?
3. How does the population change if the doubling time is reduced to 50 years?
4. Can this model be applied to predict population declines?
5. How can logarithms help in finding the time needed to reach a certain population?

**Tip**: Exponential growth models are widely used in population studies, finance, and biology due to their ability to represent rapid changes over time.

A barangay has 1,000 individuals and its population doubles every 60 years. Give an exponential model for the barangay. What is the barangay’s population in 10 years?

Learn how to model the population growth of a barangay with 1,000 individuals, doubling every 60 years, using an exponential growth model. This solution explains how to calculate the population after 10 years, using the formula P(t) = 1,000 * 2^(t/60). Suitable for Grades 10-12.

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