Question

You realize these results are too good to be true as time goes on. You recall from your biology class that there are a variety of factors that tend to constrain population growth, and that there is likely a carrying capacity for your lake. You look at other similar unattended lakes in the area that have had trout in them for years. The Fish and Wildlife Department estimates the trout populations of these small lakes to be about 200. You have decided to model the environmental constraints to the population growth rate with the linear expression 40 (1/5) y. You feel a better D.E. representing the trout population growth rate in your lake is given by(1/20) (40- (1/5)y) 10. Sketch by hand on your paper the solutions to the D.E. in the ty-plane with initially 50 trout introduced and initially 250 trout introduced. Don't forget your scales 11. From Euler's Method, for the approximation with initially 50 trout, state the two points closest to the y-value 140. (Recall: Winplot has the table button.) Next state the equation of the straight line that runs through these two points 2 12. Use the equation of the line to approximate when the fish population will reach 140 trout. (Give four decimal places.)

Answer 1

Solution:

hePane wtk inkaly 50 out inbro duced n kally 25o trout tnkeoduced and d t loo LOO 2 O- (n:6 alt y.50 trous rntro duced, y(o)-50 are 5 0 200 -50

deffevential exuat on 5 2. 1(3 2. e 200 For Ct();- nially, 25o trous oure infro duced <| Co) - 25 0 25 0 5 950 -Re d溜eenkal ty.akonis,