Question 891849: A culture of bacteria obeys the law of uninhibited growth. If 140,000 are present initially and there are 609,000 after 6 hours. How long will it take to reach 1,000,000?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A culture of bacteria obeys the law of uninhibited growth.
If 140,000 are present initially and there are 609,000 after 6 hours.
How long will it take to reach 1,000,000?
:
An exponential growth formula
Ao*e^(kt) = A, where
Ao = initial amt
t = time of growth
k = exponential constant
:
Using 1000's bacteria; one million = 1000
140*e^(6k) = 609
e^(6k) = 609/140
ln(e^6k) = ln(609/140)
6k*ln(e) = 1.47
ln of e = 1
6k = 1.47
k = 1.47/6
k = .245
:
time required to have one million
140*e^(.245t) = 1000
ln(e^(.245k)) = ln(1000/140)
.245t = 1.966
t = 1.966/.245
t = 8.02 ~ 8 hrs to have 1 million bacteria
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