Exponential problem with E. coli

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In summary, the conversation is discussing a mathematical model for the number of parts per million of E. coli in a stream after a pollutant containing E. coli is introduced. The model is represented by x(t) = loge (t + e2) and t represents the time in hours after the introduction. The question asks for the initial number of parts per million of E. coli introduced and the time at which the introduction takes place. After some discussion, it is determined that the initial number is 2 ppm and the introduction takes place at t=0.
  • #1
rachael
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20 The number of parts per million, x, of E. coli in a stream t hours after a pollutant containing E. coli is introduced is modeled by
x(t) = loge (t + e2), t ≥ 0.
a How many parts per million of E. coli are introduced into the stream?
how do i work out this question?
 
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  • #2
At what time t does the introduction of E coli take place?

Regards,
George
 
  • #3
I'm assuming you know the laws of logs? How far have you worked through the problem?
 
  • #4
thank you . ...
 
  • #5
i let t=0 therefore loge e2 equals to 2 is it correct?
 
  • #6
rachael said:
i let t=0 therefore loge e2 equals to 2 is it correct?

2 ppm, yes. Nice work!

Regards,

Rich B.
 

FAQ: Exponential problem with E. coli

What is an exponential problem with E. coli?

An exponential problem with E. coli refers to the rapid growth and reproduction of the bacteria, which can lead to a large increase in population size in a short period of time.

How does E. coli cause exponential growth?

E. coli has a short generation time and can reproduce quickly under favorable conditions, leading to exponential growth. It also has the ability to transfer genetic material between cells, allowing for rapid evolution and adaptation to new environments.

What are the potential consequences of an exponential problem with E. coli?

If not properly controlled, an exponential problem with E. coli can lead to outbreaks of foodborne illness, contamination of water sources, and antibiotic resistance. It can also cause economic losses in industries such as agriculture and healthcare.

How can an exponential problem with E. coli be prevented or controlled?

Prevention and control measures for an exponential problem with E. coli include proper sanitation and hygiene practices, thorough cooking of food, and the use of antibiotics only when necessary to reduce the risk of antibiotic resistance. Regular testing and monitoring of E. coli populations can also help detect and prevent potential outbreaks.

Is an exponential problem with E. coli a common issue?

Yes, E. coli is a common bacteria found in the environment and in the digestive tract of animals and humans. While most strains of E. coli are harmless, certain strains, such as E. coli O157:H7, can cause serious illness and outbreaks. Therefore, it is important to understand and address exponential growth of E. coli populations to prevent potential health and economic consequences.

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