Population growth using logarithims

In summary, the conversation revolves around solving for the doubling period of a culture starting with 100,000 bacteria and growing to 125,000 bacteria after 20 minutes. The equation used is Current=Original(rate)^time and the rate is found to be 1.01. By taking the 20th root of 1.25, the doubling period is calculated to be 62 minutes. The conversation ends with the person thanking the other for guiding them in the right direction.
  • #1
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4
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Homework Statement



A culture begins with 100,000 bacteria and grows to 125,000 bacteria after 20 min. What is the doubling period to the nearest minute?

Homework Equations



Current=Original(rate)^time

The Attempt at a Solution



I can get make the first part out. 125000=100000(rate)^2 I have a feeling its wrong but its as far as i can get.
 
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  • #2
Well, yeah. The doubling period is time, and it's supposed to be the thing you're solving for.
 
  • #3
So would my rate be 2? if so then would this be right 120000=100000(2)^t
1.25=2^t
log1.25/log2=t?

What confuses me is when it says doubling period, is that time or the rate?
 
  • #4
Well, start with this:

The original is 100,000 and it changes to 125,000 in 20 minutes. So, first solve for the rate, then put in the rate to the equation 200,000=100,000(rate)^(time)
 
  • #5
Well i can get this far but i can't get farther sorry.
125000=100000(rate)^20
125000/100000=r^20
log (125000/100000)=20log r

I don't know how to go farther, if r had a value and i was solving for time i would have no problem with this.
 
  • #6
alrighhhht worked it out on my own :)

I figured, why log to find the rate, 20th root it.

125000/100000=r^20
(20th root) 1.25=r
r=1.01

200000=100000(1.01)^t
2=1.01^t
log 2/log1.01=t
t=62 minutes which is the answer in the back of my textbook. Thanks for setting me on the right path Char.Limit :D
 
  • #7
No problem. And it's true... roots are almost always easier than logs.
 

Related to Population growth using logarithims

1. What is population growth using logarithms?

Population growth using logarithms is a mathematical model that describes the relationship between population growth and time. It is based on the principle of exponential growth, where the population increases at a constant rate over time.

2. How is logarithmic growth different from linear growth?

Logarithmic growth is different from linear growth in that it increases at an accelerating rate, while linear growth increases at a constant rate. This means that in logarithmic growth, the population grows faster and faster as time goes on, while in linear growth, the population grows at a constant rate.

3. What factors affect population growth using logarithms?

There are several factors that can affect population growth using logarithms, including birth rate, death rate, immigration, and emigration. These factors can change the rate of growth and cause fluctuations in the population over time.

4. How can population growth using logarithms be used to predict future population trends?

By using historical population data and applying the principles of logarithmic growth, scientists can make predictions about future population trends. This can help governments and organizations plan for future resource needs and potential challenges related to population growth.

5. What are the limitations of using logarithmic growth to study population growth?

While logarithmic growth is a useful model for understanding population growth, it does have limitations. It assumes a constant growth rate, which may not always be the case in real-world populations. Additionally, it does not take into account external factors such as natural disasters or human interventions that can significantly impact population growth.

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