Question

The population of a country increased by an average of 2% per year from 2000 to 2003. If the population of this country was 2,000,000 on December 31, 2003, then the population of this country on January 1, 2000, to the nearest thousand would have been

A. 1,846,000
B. 1,852,000
C. 1,000,000
D. 1,500,000

Answer 1

A population of size P increasing at the rate of 2% may be modelled as follows 

P = P0 e0.02 t , where t is the number of years after t = 0 and P0 is the population at t = 0. 

Let t = 0 corresponds to January 1, 2000 and therefore t = 4 corresponds to December 31. But P is 2,000,000 when t = 4. Hence 

2,000,000 = P0 e0.02*4

Solve the above for P0 

P0 = 2,000,000 / e0.02*4 = 1 846 000 (rounded to the nearest thousand) 

P0 is the population at t = 0 or on January 1, 2000.

A. is the correct answer