SOLUTION: City A and B lead a population of 70,000 and 60,000 respectively. At January 01 2001 city A grows at a rate of 5% per year and B grows at 4%. Find the difference between their popu

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: City A and B lead a population of 70,000 and 60,000 respectively. At January 01 2001 city A grows at a rate of 5% per year and B grows at 4%. Find the difference between their popu      Log On


   

Question 763257: City A and B lead a population of 70,000 and 60,000 respectively. At January 01 2001 city A grows at a rate of 5% per year and B grows at 4%. Find the difference between their population at the end of December 2003.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A's rate of growth = 5% / yr
B's rate of growth = 4% / yr
Let +n+ = number of years passed
since Jan 2001
Let +P+ = population
---------------
Equation for A:
(1) +P+=+70000%2A%28+1+%2B+.05+%29%5En+
Equation for B:
(2) +P+=+60000%2A%28+1+%2B+.04+%29%5En+
---------------------
From 2001 to 2003 is 2 years
The difference in their populations in 2 years is
+70000%2A%28+1+%2B+.05+%29%5En+-+60000%2A%28+1+%2B+.04+%29%5En+
+70000%2A+1.05%5E2+-+60000%2A1.04%5E2+
+70000%2A1.1025+-+60000%2A1.0816+
+77175+-+64896+=+12279+
at the end of December 2003, A's population
will be 12,279 greater than B's