Question

In 2016, country A has a population of 20,672,987 and growth of 3.81%.

In 2016 country B has a population of 185,989,640 and has a growth of 2.58%

If the population growth doesn't change, what year will they have the same population, and how large is it?

Answer 1

After x years, you have
20672987*1.0381^x = 185989640*1.0258^x
(1.0381/1.0258)^x = 185989640/20672987
1.01199^x = 8.99675
x = log(8.99675)/log(1.01199) = 184.32089
check:
20672987*1.0381^184.32089 = 2.035*10^10
185989640*1.0258^184.32089 = 2.035*10^10

The numbers work, but do you really think they'll grow to 20 billion? Better check the numbers again. I think you may have dropped a digit from A's population, as B is 9 times as big starting out, and the growth rates are very close, thus taking 184 years to equalize.

Answer 2

Thanks oobleck. I double checked what they wrote and indeed it is this. I'm guessing it's for math solution rather then a valid question. Not sure why again they did such a strange question. Always makes me get crazy like I've done something wrong here because of how they word it. ;)