The population of Barangay Siksikan is increasing at a rate proportional to its current population. In the year 2000, the population was 10,000. In 2003, it became 15,000. What was its population in 2009? In approximately what year will its population be 100,000?
To determine the population of Barangay Siksikan in 2009 and when it will reach 100,000, we can use the given information that the population is increasing at a rate proportional to its current population.
Let's start by finding the growth rate per year. We know that the population in 2000 was 10,000 and in 2003 it became 15,000. This means the population increased by 5,000 within three years. To find the average annual growth rate, we divide 5,000 by 3:
Average annual growth rate = (15,000 - 10,000) / 3 = 5,000 / 3 = 1,666.67 (approximately)
This means that, on average, the population of Barangay Siksikan increased by approximately 1,666.67 people per year.
To find the population in 2009, we can calculate the total increase from 2000 to 2009:
Total increase in population = Average annual growth rate * Number of years
Total increase in population = 1,666.67 * (2009 - 2000) = 1,666.67 * 9 = 15,000 (approximately)
Therefore, the population of Barangay Siksikan in 2009 is approximately 25,000 (10,000 + 15,000).
To determine when the population will reach 100,000, we can set up an equation using the growth rate per year:
Population in the future = Population in the initial year + (Average annual growth rate * Number of years)
100,000 = 10,000 + (1,666.67 * Number of years)
Now, we can solve for the number of years:
90,000 = 1,666.67 * Number of years
Number of years = 90,000 / 1,666.67 = 54 (approximately)
Therefore, the population of Barangay Siksikan will reach approximately 100,000 in the year 2054 (2000 + 54).