Solving Bacterial Population Growth: A Math Problem

In summary, the conversation discusses the growth rate of bacteria, which is proportional to its size and doubles every 2 days. At 10 days, the population is 1000 but the initial bacteria count is not given. The conversation includes an equation and a method to solve for the constant, which can be simplified to P(t) = (5/2) 2t/2.
  • #1
Hussam Al-Tayeb
5
0
If all I have given is that
1. Bacteria grows at a rate proportional to it's size.
2. It doubles in 2 days.
3. At 10 days, population is 1000.

I'm not given the initial bacteria count, I need help setting up the equation.

I did:
dy/dt = ky => dy/y = kdt => lny= kt + c => y=e^(kt) + c

y(10)= 1000 = e^(10k) + c

But I'm lost how to complete this. Any idea?
 
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  • #2
Hussam Al-Tayeb said:
lny= kt + c => y=e^(kt) + c
Look on the right side, you neglicted the constant.
 
  • #3
so it should be y=ce^(kt)

y(o) = c e^0 = c
then y(2) = c e^(2k) = 2 * y (0)
=> 2k = ln(2) => k = ln(2) / 2

now y(10) = 1000 = c e^(10k)

=> c = 1000 / (e^(5ln2))

correct?
 
  • #4
Yes! great job, keep up the good work! very good.
 
  • #5
Of course, it would have been much simpler to argue that, since the population doubles every 2 days, we must have P(t)= C2t/2 where t is in days. Then P(10)= C 25= 1000 so C= 1000/32= 100/16= 10/8= 5/2.

P(t)= (5/2) 2t/2.

(But Antineutron is right- great job!)
 

What is bacterial population growth?

Bacterial population growth refers to the increase in the number of bacteria in a given population over time. This growth is influenced by various factors such as nutrient availability, temperature, and competition with other organisms.

Why is it important to solve bacterial population growth math problems?

Solving bacterial population growth math problems allows us to better understand and predict how bacteria will respond to changes in their environment. This information is crucial for developing strategies to control and prevent bacterial infections.

What are the key variables in the mathematical model for bacterial population growth?

The key variables in the mathematical model for bacterial population growth include initial population size, growth rate, carrying capacity, and time. These variables help to determine how the population will change over time.

How can mathematical models be used to study bacterial population growth?

Mathematical models can be used to simulate and analyze different scenarios of bacterial population growth. By manipulating the values of the variables, we can predict how changes in the environment will affect the growth of bacteria and identify potential interventions to control their growth.

What are the limitations of using mathematical models to study bacterial population growth?

Mathematical models are simplifications of real-life situations and cannot account for all the complexities of bacterial growth. Additionally, these models rely on assumptions and may not accurately predict the behavior of bacteria in a natural setting. Therefore, it is important to validate the results of mathematical models with experimental data.

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