SOLUTION: The city of Anville is currently home to 28000 people, and the population has been growing at a continuous rate of 5% per year. The city of Brinker is currently home to 25000 peopl

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The city of Anville is currently home to 28000 people, and the population has been growing at a continuous rate of 5% per year. The city of Brinker is currently home to 25000 peopl      Log On


   

Question 1176219: The city of Anville is currently home to 28000 people, and the population has been growing at a continuous rate of 5% per year. The city of Brinker is currently home to 25000 people, and the population has been growing at a continuous rate of 7% per year. In how many years will the populations of the two towns be equal?
? years
Give your answer accurate to at least 2 decimal places.
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
 Anville is currently home to 28000 people, and the population has been 
growing at a continuous rate of 5% per year
 
 Brinker is currently home to 25000 people, and the population 
has been growing at a continuous rate of 7% per year.
A = Pe ^(rt),   
   28000e^.05t = 25000e^.07t
   28000/25000 = e^.07t/e^.05t = e^.02t
    ln(28000/25000)/.02 = t = 5.67 years

Wish You the Best in your Studies.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Population of Anville after n years: 28000e%5E%28.05n%29
Population of Brinker after n years: 25000e%5E%28.07t%29
28000e%5E%28.05t%29+=+25000e%5E%28.07t%29
28000%2F25000+=+e%5E%28.07t%29%2Fe%5E%28.05t%29
1.12+=+e%5E%28.02t%29
ln%281.12%29+=+.02t
t+=+ln%281.12%29%2F.02+=+50%2Aln%281.12%29

Use a calculator....

Or you can simply graph the two equations on a graphing calculator and find where they intersect.