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- Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?The population P = P(t) of a species satisfifies the logistic equation P'= aP(1-bP), P(0) = P0 > 0. (a) Find P for t > 0. (b) Find the limit of P(t) as t → ∞. What does this mean in terms of the population?Prove that the graph of the equation Ax2 + Cy2 + Dx + Ey + F = 0 is one of the following (except in degenerate cases).
- For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is given by T=(C/2−D/3)D^2. What dosage maximizes the temperature change? The sensitivity of the body to the drug is defined as dT/dD. What dosage maximizes sensitivity?The size P of a small herbivore population at time t (in years) obeys the function P(t)e^0.28t if they have enough food and the predator population stays constant. After how many years will the population reach 4000?At time t=0, a driver jumps from a diving board that is 25 feet high. Because the drivers initial velocity is 15 feet per second, her position function is h=-16t^2+15t+25. a) when does the diver hit the water? b) what is the divers velocity at impact?
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