Exponential Growth and Decay Models

Key Questions

• What is the general formula for exponential growth of a population?

  Answer:

  Population #[P]= Ce^[kt#

  Explanation:

  If the rate of growth #P# is proportional to itself, then with respect to time #t#,

  #[dP]/dt=kP#, ....inverting both sides, .....#dt/[dP]=[1]/[kP# and so integrating both sides

  #intdt=int[dP]/[kP#, thus,..... #t=1/klnP +# a constant............#[1]#

  Suppose #P# is some value # C# when# t=0#, substituting

  #0=1/klnC+# constant, therefore the constant #= -1/klnC# and so substituting this value for the constant in ...#[1]# we have ,

  #t= 1/k[ln P-lnC]# = #1/k ln[P/C]#, therefore , #kt=ln[p/C]#[ theory of logs] and so

  #e^[kt]=P/C#......giving # P=Ce^[kt#. The constant #k# will represent the excess of births over deaths or vice versa for a decreasing rate.

  Barry H. · 1 · Mar 2 2018

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• What is the general formula for exponential growth of a population?
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• How do you know When to use an exponential growth model?
• Question #f8df9
• Question #41ac8
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