2. [20] A population of Ladon dragons has a birth rate of 3.3 individuals / (ind

Question

2. [20] A population of Ladon dragons has a birth rate of 3.3 individuals / (individuals x year) and a death rate of 3.2 individuals / (individuals x year). (a) What is r? (b) Based on your answer from part a, is the population growing, declining, or remaining constant? (c) Assuming exponential growth, how many years are necessary for the population to double? (d) On the Wondering Rock Mountain, the population is presently 49. What will the population be in 20 years? (e) If the carrying capacity were 105 on the Wondering Rock Mountain, what would the population be in 20 years (using the logistic model)?

Explanation / Answer

a)   rate r = birth rate - death rate

              = 3.3 -3.2

              = 0.1

b) Since rate is positive, population is growing.

c) Given that exponential growth of population.

Hence,

    Nt = No e^rt

    Given that populatin to double.

    Then,

     Nt = 2 No

   So,

   2No = No e^(0.1 x t)

e^(0.1 x t) = 2

   0.1 t = 0.693

    t = 6.93 yrs = 7 yrs

Therefore,

7 years are necessary for the population to double.

d)

    Nt= No e^rt

      No = 49

      Nt = ?

      r = 0.1

      t = 20 yrs

    Hence,

    Nt= No e^rt

         = 49 x e^(0.1 x 20)

        = 362

     Nt = 362

Therefore,

population in 20 years = 362

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