Is There a Discrepancy in the Bacteria Growth Formula?

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Discussion Overview

The discussion revolves around a formula related to bacterial growth, specifically examining the derivative of the function that models this growth. Participants are analyzing the calculations and units involved in the formula, as well as potential discrepancies in the interpretation of the results.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a derivative calculation for bacterial growth, yielding specific values at different time points.
  • Another participant questions the meaning of the variables "p" and "h" in the context of the formula.
  • A third participant suggests that "p" denotes population and "h" denotes hours.
  • There is a challenge regarding the use of "population" as a unit, with a suggestion that "bacteria per hour" would be more appropriate.
  • Concerns are raised about the presence of the number "3.3" in the calculations, with a question about whether rounding was instructed.
  • Another participant provides an alternative interpretation of the derivative at specific time points, suggesting different values than those initially calculated.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the formula and the calculations involved. There is no consensus on the correct values or units, and the discussion remains unresolved.

Contextual Notes

There are limitations regarding the definitions of variables and the assumptions made in the calculations. The discussion also highlights potential misunderstandings about units of measurement and the interpretation of the formula.

Who May Find This Useful

This discussion may be useful for individuals interested in mathematical modeling of biological processes, particularly in understanding bacterial growth and derivative calculations.

karush
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$\tiny{205.22}$
$$\displaystyle
b'(t)=8^5-2(8^4)(t) \\
b'(0)=8^5-2(8^4)(0)=8^5=3.3 \cdot 10^4 \, \frac{p}{h} \\
b'(4)=8^5-2(8^4)(4)=0 \,\frac{p}{h} \\
b'(8)=8^5-2(8^4)(8)=-8^5=-3.3 \cdot 10^4 \, \frac{p}{h}$$
$$\text{suggestions?}$$
 
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What is $p$? What is $h$?
 
My guess is he denoted "population" as p and "hours" as h.
 
yep
 
"population" is not a unit of quantity! It looks to me like the formula, which says "b= " gives the number of bacteria so a better quantity would be "bacteria per hour". In any case, I don't see any reason for the "3.3". Were you told to "round off" and give an approximate answer? The formula given is b= 8^6+ 8^5 t+ 8^4t^2. The rate of growth is given by b'= 8^5+ 2(8^4)t.

When t= 0, that is b'= 8^5. When t= 4, that is b'= 8^5+ 2(8^4)(4)= 8^5+ 8(8^4)= 2(8^5). When t= 8, that is b'= 8^5+ 2(8^4)(8)= 8^5+ 2(8^5)= 3(8^5).
 

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