The population of the country increased by an average of 2% per year from 2000 to 2003. To find the population in 2000, we need to calculate the population increase over the 3-year period.
Let's assume the population on January 1, 2000, is P.
From 2000 to 2001, the population would have increased by 2% of P, which is 0.02P.
So, on January 1, 2001, the population would be P + 0.02P = 1.02P.
Similarly, from 2001 to 2002, the population would have increased by 2% of 1.02P, which is 0.02(1.02P) = 0.0204P.
So, on January 1, 2002, the population would be 1.02P + 0.0204P = 1.0404P.
Finally, from 2002 to 2003, the population would have increased by 2% of 1.0404P, which is 0.020808P.
So, on January 1, 2003, the population would be 1.0404P + 0.020808P = 1.061208P.
Given that the population on December 31, 2003, is 2,000,000, we can set up the equation:
1.061208P = 2,000,000
Solving for P, we get P ≈ 1,846,000. Therefore, the population on January 1, 2000, to the nearest thousand would have been 1,846,000.