SOLUTION: The bacteria in a certain culture double every 7.1 hours. The culture has 6,500 bacteria at the start. How many bacteria will the culture contain after 4 hours?

Question 702020: The bacteria in a certain culture double every 7.1 hours. The culture has 6,500 bacteria at the start.
How many bacteria will the culture contain after 4 hours?
Found 2 solutions by ankor@dixie-net.com, nerdybill:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The bacteria in a certain culture double every 7.1 hours.
The culture has 6,500 bacteria at the start. How much after 4 hrs
:
Using the formula: A = Ao*2^(t/d) where
A = amt after t time
Ao = initial amt (t=0)
t = time of action
d = doubling time of the bacteria
;
A = 6500*2^(4/7.1)
A = 6500 * 1.4777
A = 9605 bacteria after 4 hrs
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The bacteria in a certain culture double every 7.1 hours. The culture has 6,500 bacteria at the start. How many bacteria will the culture contain after 4 hours?
.
General exponential growth/decay equation:
A = Pe^(rt)
where
A is amount after time t
P is initial amount
r is growth/decay rate
t is time
.
From: "The bacteria in a certain culture double every 7.1 hours." we can determine r:
P/2 = Pe^(r*7.1)
1/2 = e^(r*7.1)
.5 = e^(r*7.1)
ln(.5) = r*7.1
ln(.5)/7.1 = r
-0.09763 = r
.
Now, we can answer:
How many bacteria will the culture contain after 4 hours?
A = Pe^(rt)
A = 6500e^(-0.09763*4)
A = 6500e^(-0.3905055)
A = 4398.65 (answer)

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