The country of the Bahamas stopped allowing long-lining fishing in 1990 and comp

Question

The country of the Bahamas stopped allowing long-lining fishing in 1990 and completely banned shark fishing in 2011. The nearby country of Belize still allows both long-lining and shark fishing. If each country had a population of 2,000 sharks in 2011 and both had a carrying capacity of 11,000 sharks, what would the population size be in 2017? Estimate for the population growth rate in the Bahamas in 05 while that in Belize in -.02. (Show the equation you are using and at least some of your work for full credit). Let's imagine that in 2020, the government of Belize decides to make long-lining and shark fishing illegal. Because the population would be so low, it can basically grow exponentially for 20 years. What would the population size be in 2040? (Show the equation you are using and your work for full credit.).

Explanation / Answer

ans 6a: We can use the logistic growth rate equation for this question. The formula is :

dN/dt = rmax N (K-N)/K

here change is computer from 2011 to 2017 therefore, 6 years = dt r = .05, therefore for bahamas, it would be -

dN/ 6 = .05 x 2000 (11,000-2000) / 11,000

dN= 81 x 6

dN = 486 for Bahamas therefore population in 2017 would be 2000 + 486 = 2486

For Belize, it would be:

dN/6 = -.02 x 2000 (11,000 - 2000)/ 11,000

dN = -194.4

therefore population in 2017 would be 2000 - 194.4 = 1805

ans 6 b - The population in Belize in 2020 would be:

dN/ 3 = -.02 x 1805 ( 11000-1805) / 11000

dN = -89.88 or -90

therefore 1805 - 90 = 1715.

now we allow it grow exponentially for 20 years so we use the formula:

dN/dt = rN

dN/ 20 = 0.02 x 1715

dN = 686

therefore after 20 years in 2040 the population in Belize would be 1715 + 686 = 2401

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