Answer:
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.