How Is Doubling Time Calculated in Population Growth Models?

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SUMMARY

The discussion focuses on calculating the doubling time in population growth models using the formula N = N0e^kt, where k is defined as 1/20 ln(5/4). Participants clarify that to find the doubling time, one should set N = 2N0 and apply the natural logarithm to both sides of the equation. This approach confirms that the doubling time remains consistent regardless of the initial population value. The key takeaway is the importance of substituting the correct values into the formula and simplifying accordingly.

PREREQUISITES
  • Understanding of exponential growth models
  • Familiarity with natural logarithms
  • Basic algebra skills for manipulating equations
  • Knowledge of the concept of doubling time in population studies
NEXT STEPS
  • Study the derivation of the exponential growth formula N = N0e^kt
  • Learn how to apply natural logarithms in population growth calculations
  • Explore different population growth models beyond the exponential model
  • Investigate real-world applications of doubling time in demographics
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Students in mathematics or biology, researchers in demographic studies, and anyone interested in understanding population dynamics and growth calculations.

Christo
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1. The population of a certain country grows according to the formula:

N = N0e^kt

Where N is the number of people (in millions) after t years, N0 is the initial number of people (in millions) and k = 1/20 ln 5/4.

Calculate the doubling time of this population. Leave your answer in terms
of ln : Do not use a calculator.2. I don't understand where to start off.3. I have basically come to the conclusion that N = 2N0
That is how far I have come. I know I haven't done anything as of yet. But any help would be appreciated
 
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Well, you were given a value for k. Did you plug this value into the population equation and make any obvious simplifications?
 
Use N=2 and No=1.
Take natural log of both sides of the equation.
 
Thanks for the info, will plug in the variables and see where I end up.
 
To see that you get the same "doubling time" for any initial value, take N= 2N_0.
 

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