SOLUTION: A towns population grows at the rate of 13% per year. If this grown rate remains how long will It take the population to double. Round to the nearest tenth

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A towns population grows at the rate of 13% per year. If this grown rate remains how long will It take the population to double. Round to the nearest tenth       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1028864: A towns population grows at the rate of 13% per year. If this grown rate remains how long will
It take the population to double. Round to the nearest tenth

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +A+ = the population at the start
Let +t+ = years it takes population to double
+2A+ = the population after +t+ years
+r+=+.13+ = yearly rate of increase
-------------------------------
The formula is:
+2A+=+A%2A%28+1+%2B+.13+%29%5Et+
Divide both sides by +A+
+2+=+1.13%5Et+
Take the log of both sides
+log%282%29+=+t%2Alog%28+1.13+%29+
+t+=+log%282%29+%2F+log%28+1.13+%29+
+t+=+.30103%2F.05308+
+t+=+5.671+
In 5.7 yrs the population will be
double what it started as.
---------------------------
check:
+2+=+1.13%5Et+
+2+=+1.13%5E5.671+
+2+=+1.999898+
close enough