4. A tank initially contains pounds of salt dissolved in 200 gallons of water. Starting at time t=0, water containing a half pound of salt per gallon enters the tank at a rate of 4 gallons per minute and a well stirred solution leaves the tank at the same rate. If c(t) represents the concentration of salt in the tank at time t, show that the limiting concentration (as t grows large) is a half-pound per gallon. That is, show that c(t).
5. In 1980 the population of alligators on the Kennedy Space Center grounds was estimated to be 1500. In 2006 the population had grown to an estimated 6000.
(A). Using the Malthusian Law for population growth, estimate the population of the alligators on the ground in 2020.
Malthusian Law:
(B). Suppose we have the additional estimate that in 1993, the population was 4100. Using the logistic model, estimate the population in 2020.
6.
Initial Value
2
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tiffy
problem_set_3.docx
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