How Does Bacterial Population Change Over Time?

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Discussion Overview

The discussion revolves around the relationship between bacterial population growth and time, specifically examining how the population changes at regular intervals. Participants explore mathematical models to describe this growth, including exponential and logarithmic equations, as well as geometric sequences.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant presents a series of bacterial population measurements over time, suggesting a need for an equation to describe the relationship.
  • Another participant observes that the population appears to exhibit exponential growth, noting that it doubles every 30 minutes.
  • A different participant proposes that logarithmic equations could also be applicable, as they are related to exponential equations.
  • Another contribution highlights the similarity of the situation to a geometric sequence, emphasizing the need for an adjustment in the exponent to accurately reflect the initial population of 1000.
  • One participant reiterates the population doubling every 30 minutes and attempts to formulate a general equation for the population at any time t.

Areas of Agreement / Disagreement

Participants generally agree that the population growth is exponential and that it doubles at regular intervals. However, there is no consensus on the exact mathematical formulation or the best model to use, as different approaches are suggested.

Contextual Notes

Some participants note the need for adjustments in the mathematical expressions to accurately represent the initial conditions and the nature of the growth, indicating potential limitations in the proposed models.

mahi687
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i guess I am trying to find the relationship between population growth and time.

bacteria population is 1000 during time 0minutes.
bacteria p.: 2000 time: 30 minutes
bacteria p.: 4000 time: 60 minutes
bacteria p.: 8000 time: 90 minutes
bacteria p.:16000 time: 120 minutes

What is the equation for the relationship between the two?
 
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Simple visual inspection of the ordered pairs indicates exponential growth. Your example begins with 1000 units, and doubles (multiplication by 2) every 30 minutes. Check your intermediate algebra book for the chapter or section on exponential growth.
 
You could also use a logarithmic equation as they are basically the same as exponential equations.
 
A clearer way to understand this population growth exercise is that your exponent is a whole number for every 30 minute time passage; this means something like n/30, where n is for minutes after zero-time. Further, this exercise is like a geometric sequence in which the first term is 1000. The common ratio is obviously 2 (but in fact the "exponent" needs a bit of adjustment if you wanted the first term to actually be 1000; do you know what this adjustment is?)

Note carefully, I say is "like" a geometric sequence. Not "is" a geometric sequence. In the given case, the independent variable can be continuous.
 
Last edited:
mahi687 said:
i guess I am trying to find the relationship between population growth and time.

bacteria population is 1000 during time 0minutes.
bacteria p.: 2000 time: 30 minutes
bacteria p.: 4000 time: 60 minutes
bacteria p.: 8000 time: 90 minutes
bacteria p.:16000 time: 120 minutes

What is the equation for the relationship between the two?

The population doubles every 30 minutes.

P(0)= 1000.
P(30)= 1000(2)= 1000(230/30).
P(60)= 1000(4)= 1000(22)= 1000(260/30).
P(90)= 1000(8)= 1000(23)= 1000(290/30).
P(120)= 1000(16)= 1000(24)= 1000(2120/30).

so P(t)= ?
 

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