MathBench > Population Dynamics

Bacterial Growth:
The E. coli ate my homework

Extended problem #2: Exponential growth ends (with a whimper)


Enough with the cute little stories. The last few pages are all biology, all the time. I put some of the basic exponential growth information in the box to the right, and the rest is for you to figure out.

Helpful Info on
Exponential Growth:

Nt = N0 * 2g

Nt = N0 * e(mt)

m = ln(2)/doubling time

As you know, bacterial cultures go through several growth phases. In the beginning, when resources are extremely plentiful, bacteria grow exponentially, but growth slows as the environment gets more crowded and resources are harder to find. Eventually as resources get used up, the population levels out and then declines. So, your job is to figure out when the exponential part of growth is over.

You have been given a mystery bacteria and growth medium by your instructor. Your instructions are 1) to determine the exponential growth rate of this bacteria, and 2) to determine how long the medium continues to support exponential growth. Specifically, you will know when the bacteria are no longer growing exponentially because their population size is less than 90% of what would be predicted by exponential growth.

Here is the data from your growth experiment:

time popn
0 min 4.3 * 106
20 min 9.7 * 106
40 min 22 * 106
60 min 48 * 106
80 min 97 * 106
100 min 116 * 106
120 min 118 * 106
140 min 67 * 106

 

Just look at the data first... what can you see with your bare eyes, so to speak?

About doubling time:

About the general shape of the population trajectory:

About when growth begins to slow down:

What is the growth rate? (this is a simplified way to calculate the growth rate -- you can also review page 9 for how to calculate doubling rate, and use that to get the growth rate)

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I think I have the answer: ln(9.7/4.3) / 20= 0.041 per min

 

What should the population be at the third time measured?

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I think I have the answer: 4.3 * 106 * e0.041*40 = 2.22 * 107

 

When did exponential growth stop?

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I think I have the answer: time = 80 min