Micro, math help

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My Micro instructor is trying to teach us how to determine different ways of bacterial growth and math is not my strong point. He gave us some sample problems and I think I have figured out how to do a couple of them but I am really having trouble with the other ones. I need to figure out how to do these, I'm sure one or two will be on the final exam in August. Can some one help me out? Heres the examples.

A coconut cream pie is contaminated with 20 cells or Staphylococcus aureus, the bacterium has a generation time of 30 minutes. How many cells will be present after the pie sits at room temperature for 3 hours?

This is the answer that I got.

20 cells

30 g time

3 hours

X=20x2(6)

20, 40, 80, 160, 320, 640 ,1280

My answer is 1280 cells are present in the pie after 3 hours.

This is the one I am having problems with. I don't know where to start with the math.

An overnight culture os Salmonella typhimurium, which has a generation time of 20 minutes is diluted 1,000 fold. Samples of the dilution are spread on agar plates, incubated for 18 hours at 25C, then counted, yielding colony counts of 50, 59, and 77. What is the viable cell concentration or the original culture?

Can some one please help me with this. Grrr I hate math.

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It depends on how delicious the coconut cream pie is.

That's the extend of my knowledge.

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Specializes in SRNA.
A coconut cream pie is contaminated with 20 cells or Staphylococcus aureus, the bacterium has a generation time of 30 minutes. How many cells will be present after the pie sits at room temperature for 3 hours?

This is the answer that I got.

20 cells

30 g time

3 hours

X=20x2(6)

20, 40, 80, 160, 320, 640 ,1280

My answer is 1280 cells are present in the pie after 3 hours.

You're right. If you take the original number of cells and multiply by 2 to the power of the number of generations, you get the answer. So, 20x2^6 = 20x64 = 1280.

If the pie was contaminated by 75 cells with 20 minute generation times and sat there for 4 hours, there would be 12 generations. So, 75x2^12 = 75x4096 = 307200.

The second example you gave, I'm not sure how to find an answer, because it would depend on how much of the dilution sample was plated. Like, if the original sample had 20,000 cells, a 10x dilution would have 2000, a 100x dilution would have 200, and a 1000x dilution would have 20. Let's say each dilution sample was 5mL in volume. If you plated 1mL of the 1000x dilution, you should get around 4 colonies after incubation, but if you plate 250 microliters you'd only get 1. So, the volume plated would influence how you determine the original cell concentration...unless I'm totally missing something.

Was a volume of the dilution plated provided?

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Thanks guys, I hope that I can figure the rest of the examples out. If anyone else has something to add please feel free to do so.

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Specializes in Nursing assistant.

Your salmonella question:

remember you are dealing with exponential growth, where the bacteria doubles every 20 minutes. You can calculate what the total culture concentration is in the last generation, so you need to extrapolate backwards: if I have "x" cells at generation "n", what did I have at generation zero, so to speak. Would that be the "n"th root of "x"?

If the bacterial population doubles at regular intervals : 1, 2, 4, 8..... in a sense you are dividing this at the same intervals, 8, 4, 2, 1....

I got to think about this....

Oh yeah, and the dilution factor....

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Specializes in ICU-CVICU.

Michelle,

Did you get an answer like 6.2 x 10^4 as the original count per ml? I think you can safely assume that the amount plated was 1ml?

May

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