Quiz Solution for Mathematics 172 - Population Dynamics of Tilapia - Prof. Re Howard, Quizzes of Mathematics

Download Quiz Solution for Mathematics 172 - Population Dynamics of Tilapia - Prof. Re Howard and more Quizzes Mathematics in PDF only on Docsity! Mathematics 172 Quiz #4 You must show your work to get full credit. A population of tilapia is harested so that it has a growth rate of r = −.05 (fish/week)fish. (a) If the population is stocked at the rate of 20 fish/weel, what is the size of the stable population? (b) At what rate should the population be stocked to give a stable population of 150? Solution for (a): If S is the stocking rate, then population size, Nt, satisfies Nt+1 = (1 + r)Nt + S. In our case r = −.2 and S = 20, so this becomes Nt+1 = .8Nt + 20. When the population reaches its stable size, we have Nt+1 = Nt and thus Nt = .8Nt + 20 which is the same as .2Nt = 20 and thus the stable population size is Nt = 20 .2 = 100. Solution for (b): The set up is the same, other than we don’t know the stocking rate S. So the equation is Nt+1 = .8Nt + S. To get the stable population size, we set Nt+1 = Nt and solve: Nt = .8Nt + S which has the solution Nt = S .2 . As we want this to be 150 we set S .2 = 150 so the stocking rate is S = (.2)150 = 30