Bacterial Growth: Finding the Initial Size and Doubling Period

[Easy_as_Pi]

Homework Statement

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?

Homework Equations

P₀= 900/e^15k=1400/e^30k
P_t=P₀e^kt

The Attempt at a Solution

First, I solved for P₀, 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. I am 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?

 

[lanedance]

i've quickly checked you work and agree with your results. Also your doubling rate is consistent with the problem.

the only thing i could guess is maybe the growth rate/time is given in different units (eg. per hour) or maybe greater accuracy, though the way the problem ios written i doubt those?

 

[dynamicsolo]

Yes, this is yet another example of what I hate about computer-based education. Your growth constant has units of min^-1 , so your doubling time will have units of minutes. Is that the unit that is asked for in WebWork's question? (One of the many little things students can trip over in these systems...)

It is also possible that the answer the computer calculates is wrong (caused by the code using a formula with an error in it) or that the instructor forgot to set a tolerance for acceptable answers. (We had a problem with such a system some years back, where the default on precision was 0% and the instructor forgot to set it to 2% for that problem. Since the computer calculated all the answers to 16 digits of precision, the odds that a student would match the computer's result were extremely low...)

If you are using the units the computer wants, and other students encounter the same difficulty, alert your instructor. We run into situations like this where I am at least once per course per semester...