# Answer on Algebra Question for Allie

Question #11454

Subject: Exponential and Logarithmic functions

Question:

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?

Question:

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?

Expert's answer

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.

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.

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