SOLUTION: McPeakland has a population of 145,000 people. Every year its population triples. Staceyville's population is unknown, but its population doubles every year. After 24 years, McPeak

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: McPeakland has a population of 145,000 people. Every year its population triples. Staceyville's population is unknown, but its population doubles every year. After 24 years, McPeak      Log On


   

Question 529719: McPeakland has a population of 145,000 people. Every year its population triples. Staceyville's population is unknown, but its population doubles every year. After 24 years, McPeakland's population and Staceyville's population are the same. What is Staceyville's original population?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Staceyville's original population
Let +n+ = number of years passed
after 1 yr - 2s
after 2 yrs - 4s
after 3 yrs - 8s
+s%2A2%5En+ is population after n years
---------------
Mc Peakland's population after n yrs is
+145000%2A3%5En+
---------------
given:
+s%2A2%5E24+=+145000%2A3%5E24+
+s+=+145000%2A%283%5E24%2F2%5E24%29+
+s+=+145000%2A%283%2F2%29%5E24+
You can solve this with logs
+log%28s%29+=+log%28145000%29+%2B+24%2Alog%28+1.5+%29+
+log%28s%29+=+log%281.45%29+%2B+log%28+10%5E5%29+%2B+24%2Alog%28+1.5+%29+
+log%28s%29+=+log%281.45%29+%2B+5+%2B+24%2Alog%28+1.5+%29+
You can finish- can't find calculator