SOLUTION: Happy Holidays I have two that I am can not figure out could you please help thanks If bacteria cultures increase at a rate of 8.66% in an hour, how long will it take the c

Question 550083: Happy Holidays I have two that I am can not figure out could you please help
thanks

If bacteria cultures increase at a rate of 8.66% in an hour, how long will it take the culture to quadruple in size?
35 hours 46 hours
12 hours 16 hours
those are my choices (multiple choice)

logb x = 3.1, logb y = 2.5, logb z = 2.2
Evaluate:
logb x^4y^2/√z

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If bacteria cultures increase at a rate of 8.66% in an hour, how long will it take the culture to quadruple in size?
-----------
Amount = start*(1 + 0.0866)^t (t in hours)
Amount/start = 4
----
4 = (1.0866)^t
log(4) = t*log(1.0866)
t = log(4)/log(1.0866)
t =~ 16.69 hours
----------------------
logb x = 3.1, logb y = 2.5, logb z = 2.2
Evaluate:
logb x^4y^2/√z
------------
= 4*log(x) + 2log(y) - (1/2)log(z)
Just add those.
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