SOLUTION: Hi. I need help with this LOG problem. I've figured out a) but I'm not sure what to do for b). Your help is appreciated. Thank you. On the planet Maximillian live Sprogs and Gra

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi. I need help with this LOG problem. I've figured out a) but I'm not sure what to do for b). Your help is appreciated. Thank you. On the planet Maximillian live Sprogs and Gra      Log On


   

Question 712352: Hi. I need help with this LOG problem. I've figured out a) but I'm not sure what to do for b). Your help is appreciated. Thank you.
On the planet Maximillian live Sprogs and Graks. Initially there were 1600 sprogs and 200 Graks. The population of Sprogs doubles every 14 years and that of Graks doubles every 7 years.
a) How many Graks were there after 3 1/2 years?
Answer: 282.842712475 Graks
b) When are there as many Sprogs as Graks?
____________ years later
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +S+ = population of Sprogs
Let +G+ = population of Groks
Let n+ = number of years after initial count
For Sprogs, the formula is:
+S+=+1600%2A2%5E%28+n%2F14+%29+
For Graks,
+G+=+200%2A2%5E%28+n%2F7+%29+
-------------------------
(a)
After +3.5+ years,
+G+=+200%2A2%5E%283.5%2F7%29+
+G+=+200%2A2%5E.5+
+G+=+200%2A1.414+
+G+=+282.8+ ( you can add the extra decimals )
-------------------------
When is +S+=+G+ ?
+1600%2A2%5E%28+n%2F14+%29+=+200%2A2%5E%28+n%2F7+%29+
+8%2A2%5E%28+n%2F14+%29+=+2%5E%28+n%2F7+%29+
+2%5E3%2A2%5E%28+n%2F14+%29+=+2%5E%28+n%2F7+%29+
+2%5E%28+n%2F14+%2B+3+%29+=+2%5E%28+n%2F7+%29+
+n%2F14+%2B+3+=+n%2F7+
Multiply both sides by +14+
+n+%2B+42+=+2n+
+n+=+42+
In 42 years, their populations will be the same
check:
+1600%2A2%5E%28+42%2F14+%29+=+200%2A2%5E%28+42%2F7+%29+
+1600%2A2%5E3+=+200%2A2%5E6+
+1600%2A8+=+200%2A64+
+12800+=+12800+
OK