Question

The number of people in Barangay Sipnayan in 2012 was 670 . It is estimated that the population of this barangay increases by 50% every 2 years. What will be population of Barangay Sipnayan in 2020 ?

Answer 1

2020 3,391 Population of Baranqav Sipnayan in 2020

Explanation:

The expression for population increase is given by

Pf(x) = Pi*(1+R)^x

where Pf is the final population at year x, and Pi is the population at year 0 (starting population). R is the rate of increase per year.

In this case we have Pi = 670. To calculate the yearly increase, R, we need to examine the "50% growth every 2 years."

To achieve 50% growth, the following will be true:

Pf(x) = Pi*(1+R)^x

(1.5)*(670) = 670(1+R)^2 We can use this find the value of R required to achieve a 50% growth in 2 years, and then use that for other values of x, assuming the growth rate is constant.

The quadratic equation formed by this expression is:

670
`R^(2)` + 1340R + 335 = 0

Use the quadratic equation to find a valid solution: R = 0.2247

This means the yearly growth is 22.47%.

So the expression becomes: Pf(x) = Pi*(1+0.2247)^x

Pf(x) = (670)*(1+0.2247)^x

A full spreadsheet is attached with the results for all the years between 2012 and 2020.

Year Population

2012 670

2020 3,391