(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The count in a bacteria culture was 900 after 15 minutes and 1400 after 30 minutes.

What was the initial size of the culture? What is the doubling period? What is the size after 70 minutes? When will the population reach 11000?

2. Relevant equations

P_{0}= 900/e^{15k}=1400/e^{30k}

P_{t}=P_{0}e^{kt}

3. The attempt at a solution

First, I solved for P_{0}, and I got 578 as my answer. I know this is correct, because WebWork, in its infinite wisdom, stated it to be.

In solving for the initial population, I found my growth rate to be 0.0295

k=ln(1400/900)/15 = .0295.

Yet WebWork insists this is not the growth rate.

To find the doubling period, you merely take the natural log of 2 and divide by the growth rate.

2=e^{kt}-> ln(2)/k = t, if k =.0295, t= ln(2)/.0295 However, I am told by webwork that this answer is wrong. Im baffled as to how this is possible. If I had the wrong growth rate, I would never have been able to find the initial population value. Furthermore, I have checked P=578e^{.0295t}with the values for t=15 and t=30, and got both answers right. What am I doing wrong here? Or, per the usual, is WebWork wrong?

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# Homework Help: Diff Eq Bacterial Growth

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