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
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
