4. (6 points) Comparing Growth Equations Growth models are frequently used to st

Question

4. (6 points) Comparing Growth Equations Growth models are frequently used to study biological topics. Three classic models are given below: Exponential growth: Von Bertalanffy growth r(K Logistic growth. where r represents a growth rate and K represents a carrying capacity. In this exercise you will compare the behavior of these models with actual biological data and explore how these three models relate to one another. (a) Find a general solution to each growth equation using arbitrary r and K (b) Now find an expression for the particular solution to each growth equation with r 0.5, K 5 x 105 and 200) 1 x 104 (c) Using the math program of your choice, plot these particular solutions on the same set of axes. Label your plot, distinguish the curves with a legend, label axes. Use horizontal axis range 0 to 10 and vertical axis range from 0 to 8x105. Staple your plot to the end of the lab.

Explanation / Answer

(a) The growth solution for arbitrarary r and K are:

   Exponential Growth=> x(t)=ert+K

   Von Growth=> x(t)=K+ert+K

   Logistic Growth=> x(t)=Kert+K/(1+ert+K)

(b) The particular solution are:

  Exponential Growth=> x(t)=e500000

     Von Growth=> x(t)=500000+e500000

   Logistic Growth=> x(t)=500000e500000 / (1+e500000)

(c) The values are too large to plot on given dimensions.

(d) Logistic growth model captures better because the first two model are exponential it tends to grow exponentially but never dips.

(e) The inflection point is:

   Logistic Growth=> x=1.

(f) The curve looks before inflection point is Exponential growth model and after is logistic growth mode

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