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MathQuest2 · Dec 13, 2009, 10:36 AM

Hi, I'm kind of lost with this question. It would be awesome, if sum1 can help me out. Thanks in advance!

Question: Bacteria population doubles in 20 hours. When was the population 1/8 of its present population?

I know we have to use logs but not sure where to start!

galactus · Dec 13, 2009, 04:07 PM

Originally Posted by MathQuest2

Hi, I'm kinda lost with this question. It would be awesome, if sum1 can help me out. Thanks in advance!

Question: Bacteria population doubles in 20 hours. When was the population 1/8 of its present population?

I know we have to use logs but not sure where to start!

If the bacteria doubles in 20 hours, then we can use that to find our constant of proportionately, k. If A is the initial amount, then 2A is the amount in 20 hours.

$2A=Ae^{k\cdot 20}$

$2=e^{20k}$

$k=\frac{ln(2)}{20}$

Now, since we have k, use it to find t when A is 1/8 the present population.