Question

the population of a village has increased annually at the rate of 20%. if at the end of 3 years it is 21600, the population in the beginning of the first year?

Answer 1

The population in the beginning of the first year was approximately 12,500.

Explanation:

To find the population in the beginning of the first year, we need to work backwards from the given population at the end of 3 years using the annual growth rate.

Let's denote the population in the beginning of the first year as P. After the first year, the population would be P + 20% of P, which can be written as P + 0.2P or 1.2P.

After the second year, the population would be 1.2P + 20% of 1.2P, which can be written as 1.2P + 0.2(1.2P) or 1.2P + 0.24P or 1.44P.

Finally, after the third year, the population would be 1.44P + 20% of 1.44P, which can be written as 1.44P + 0.2(1.44P) or 1.44P + 0.288P or 1.728P.

We are given that the population at the end of 3 years is 21,600. So we can set up the equation:

1.728P = 21,600

Now, let's solve for P:

P = 21,600 / 1.728

P ≈ 12,500

Therefore, the population in the beginning of the first year was approximately 12,500.