Bacteria reproduction question?

Question

A cocci bacterium with a radius of 1 Um (1/1000 of a mm) divides every 20 minutes.  How long will it take it to go from a single cell to a group of cells that has the same mass as the earth (6x10^24 kg)?  The bacterium has the same density as water (1g/ml).

I'm completely lost here.  It's not a test question but one of our study guide qs.  The professor is kind of a dick so getting information out of him is impossible.  

Please show me HOW you go it, the correct answer is not very helpful if I can't reproduce it on test day.

Thanks!

Anonym · Accepted Answer

bacteria reproduce such: 1 * 2*10^x, with x being the number of reproduction cycles. 
Knowing that the bacteria have the same density as water, you know that the mass to volume ratio will be 1, so the volume will have to equal the same as the mass of the earth.

So you first have to determine the volume of the starting spherical cell. 4/3 pi r^3. = ~4.187 ug's

Then divide the final mass (the earth) by this number. (Dont forget to convert to equal units. so lets say 6x10^33 ug's = 2.39 x 10^32 --> thats the total number of cells.

Then just solve for x using the bacterial reproduction equation.

2.39 x 10^32 = 2x10^x
1.19 x 10^32 = 10^x
log (1.19 x 10^32) = x = 32 reproduction cycles
since each reproduction cycle (division) takes 20 mins, multiply by 20 mins.

so the final answer is about 642 minutes.

Hope that helps.

Bacteria reproduction question?

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