Population of Fish in a Lake A lake is stocked with 100 fish. Let f(1) be the number of fish after i months, and suppose that y = f(1) satisfies the differential equation y' = .0004y(1000 – y). Figure 7 shows the graph of the solu- tion to this differential equation. The graph is asymptotic to the line y = 1000, the maximum number of fish that the lake can support. How fast is the fish population growing when it reaches one-half of its maximum population? 1000 800 600 400 200 10 15 Figure 7 Growth of a fish population.
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- . On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according to thefunctionU (c, b) = 20c - c2 +18b- 3b2.How many cigars and glasses of brandy does he consume during an evening? (Cost is no objectto J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum of glasses ofbrandy and cigars consumed to 5. How many glasses of brandy and cigars will he consumeunder these circumstances?Which of the following are monotonic transformations? Please explain. 1) u = v² 2) u = lnv 3)u = -e^-vQ. 1 You are the mayor of a small town with 2000 residents. The head of your economic development agency recently conducted a survey in which the 2000 residents said that a public concert in the centre of town would be worth $20 to cach of them. Since it costs only $5000 to hold the concert, you organized and held the concert, which everyone in town enjoyed. But when you asked for donations to pay for the concert, you only collected $30 in total. What do you know? a. The survey certainly overstated how much the concert was worth to each resident. b. From the standpoint of total costs and benefits, the cost of the concert certainly exceceded the benefit. c. The concert was an example of the Tragedy of the Commons. d. Residents of the town were probably free riders.
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