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The questions and solutions for quiz 4 of math 333, which covers topics such as solving first order differential equations and population dynamics. The quiz includes finding general solutions to differential equations, modeling real-world processes with differential equations, and analyzing equilibrium solutions in population dynamics.
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You may work with other class members on this quiz, but you may not receive assistance from people not in MATH 333 (Section 002). You must show all of your work to receive full credit. Do all your work on other sheets of paper and be sure to staple all the pieces of paper together or YOU WILL GET A ‘ZERO’ ON THE QUIZ. Do not use decimal approximations unless asked to do so. Your work on this quiz must be handed in by Friday, 3 October 2008 at 1040. GOOD LUCK!
dy dt
3 y t
cos 2t t^2
a) Write an initial value problem that models this process. b) Over what time frame does the differential equation model this process? Explain.
c) Solve the initial value problem. d) At what time is the amount of salt in the tank a maximum? Give the exact solution and an appropriate estimate.
dR dt
dF dt
a) Find all equilibrium solutions of (1). b) Describe completely what happens to species F if species R is extinct. c) Describe completely what happens to species R if species F is extinct. d) Depict in the R-F plane all the information gathered above.