Barangay Sipnayan has a current population of 50,000 and the population is increasing by 3% cach year. What will be i population (approximate) in 10 years? in arithmetic sequence

The problem describes a situation of population growth, which is actually **exponential growth**, not arithmetic. An arithmetic sequence assumes a constant increase by the same amount each year, but with a 3% growth rate, the population increases by a percentage of its current amount each year.

To calculate the population in 10 years with a 3% annual growth rate, we'll use the formula for **exponential growth**:

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

Where:
- \(P(t)\) is the population after time \(t\),
- \(P_0\) is the initial population (50,000),
- \(r\) is the growth rate (3% or 0.03),
- \(t\) is the number of years (10).

Substitute the values:

\[
P(10) = 50,000 (1 + 0.03)^{10}
\]
\[
P(10) = 50,000 (1.03)^{10}
\]

Let me calculate that for you.The population of Barangay Sipnayan after 10 years, with a 3% annual growth rate, is approximately **67,196**.

Let me know if you'd like further explanation or details on this calculation!

Here are five related questions to expand on the topic:
1. What would the population be after 20 years with the same growth rate?
2. How does arithmetic growth compare to exponential growth in long-term population predictions?
3. If the population decreases by 3% each year, what will the population be in 10 years?
4. What growth rate is needed for the population to double in 10 years?
5. How can compounding interest be applied in similar population growth problems?

**Tip**: Exponential growth increases faster than arithmetic growth over time due to compounding effects!

Barangay Sipnayan has a current population of 50,000 and the population is increasing by 3% each year. What will be the population (approximate) in 10 years? in arithmetic sequence

Explore how to calculate the future population of Barangay Sipnayan, starting with 50,000 people and growing at a rate of 3% per year. This problem introduces exponential growth, applying the formula P(t) = P_0 (1 + r)^t to predict population in 10 years. Perfect for students in Grades 9-12.

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