Subject: Exponential and Logarithmic functions
In 2001 the population of X was 82 million and the population of Y was 78 million. If the populations of X and Y grow continuously at relative growth rates of- 0.15% and 1.77%, respectively, in what year will Y have a greater population than X?
Let's solve the following equation:
82*1.0015^T = 78*1.0177^T,
where T is the time that responds to equal populations X and Y.
82/78 = (1.0177/1.0015)^T ==> T = log 82/78 with base of 1.77/0.15 ≈ log 1.0513 with base 1.0162 = 3.1131 years.
So, Y will have a greater population than X in 2005 year.