# Calculating biological growth of doubling cells

For some kinds of experiments, biologists use isolated cells grown in culture. Cells differ significantly in their cell doubling times (one cell dividing into two cells).

• Plant cells can double every 18 hr
• Animal cells (matrix requiring) can double every 18 hr
• Animal cells (nonmatrix requiring)can double every 14 hr
• Yeast cells can double every 2 hr
• Bacteria cells can double every 20 min

Based on the above information, if you start with one cell of each type, how many cells of each type would you have after one week?

## Update:

I believe I can answer this the following way:

• Plant cells can double every 18 hr

18/24 = 3/4 day. 7days/ 3/4 =28/3 = 9 1/3 I disregarded the 1/3, and used the 9 doublings for 2^9= 512 cells

• Animal cells (matrix requiring) can double every 18 hr

again same as above, I got 512 cells

• there are $24\times 7$ hours in a week, divide this with the hours you mentioned and what you get, say $x$, $2^x$ will be the answers.
– user249332
Dec 9, 2015 at 22:53
• Thank you, I have updated my answer! Dec 9, 2015 at 23:20

I am not a biologist, but if I understand the problem correctly this seem to be an exponential growth problem. I believe we need to use the simple doubling time formula: $2^{\frac{d}{t}}$

where

• $d$: doubling period (time it takes for object to double in number)
• $t:$ time

Plant cells can double every 18 hr:

$=2^{\frac{(24*7)}{18}} = 2^{\frac{168}{18}} = 2^{9.3333}= 645.07$

Animal cells (matrix requiring) can double every 18 hr:

$=2^{\frac{(24*7)}{18}} = 2^{\frac{168}{18}} = 2^{9.3333}= 645.07$

Animal cells (nonmatrix requiring)can double every 14 hr:

$=2^{\frac{(24*7)}{14}} = 2^{\frac{168}{14}} = 2^{12}= 4096$

Yeast cells can double every 2 hr:

$=2^{\frac{(24*7)}{2}} = 2^{\frac{168}{2}} = 2^{84}= 1.9342813e+25$

Bacteria cells can double every 20 min:

So, notice that $20$ minutes = $0.333333$ hours:

$=2^{\frac{(24*7)}{0.333333}} = 2^{\frac{168}{0.333333}} = 2^{504.05}= 5.423645e+151$

What is matrix and non-matrix requiring? Could you provide a definition from the source?

Also review this link, it maybe related?

• What does that mean? Am I going to sleep in the street tonight? Dec 10, 2015 at 5:42
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• -IDidn'tDothat: I Did do That! Dec 10, 2015 at 6:21
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