SOLUTION: the number of bacteria in a culture increased sixfold in 10 hours. Assuming natural growth, how long did it take their number to double?

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Question 184656: the number of bacteria in a culture increased sixfold in 10 hours. Assuming natural growth, how long did it take their number to double?
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
the number of bacteria in a culture increased sixfold in 10 hours.
Assuming natural growth, how long did it take their number to double?
:
:
Let x = hourly growth constant
:
1(x^10) = 6
10*log(x) = log(6)
10*log(x) = .778
log(x) =
log(x) = .0778
x = 1.1962
:
Find the time in hrs to double (t)
1.1962^t = 2
t*log(1.1962) = log(2)
.0778t = .301
t =
t = 3.869 hrs to double
;
:
Check solution in calc: enter 1.1962^3.869 = 1.9999~ 2


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
the number of bacteria in a culture increased sixfold in 10 hours. Assuming natural growth, how long did it take their number to double?

Your textbook and teacher may be using different letters from the
ones I use, if so you can change the letters to yours.



 has gone from  to  while t increased to .  
So we substitute  for  and  for :



Divide both sides by 



Change to natural log form:







So we take the original formula
and substitute 
for r.




Now we want to find what  is when 

---




Divide both sides by 



Change to natural log form:







Edwin
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