Zombies have invaded my lab! They recruit more of the undead at the rate: dz 10 f(2) = (z – 6)(z+ 6) In(÷), dt where t is time and z is the number of zombies. Determine all biologically meaningful steady states (equilibrium points). Determine the stability of each steady state (equlibrium point) that is biologically meaningful, using the derivative test. Draw a phase-line diagram and answer: "If 9 zombies are in the lab initially, how many will there be eventually?"

A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg

Suppose that T =f(t) gives the temperature T (in degrees Fahrenheit) of a pot of coffee t minutes after being brewed. If f '(20) = -3 and f(20) = 125, use a linear approximation (linearization) to estimate the coffee's temperature after 20.4 minutes.

Suppose the number of bacteria in a culture increases by 50% every hour if left on its own. Assuming that biologists decide to remove approximately one thousand bacteria from the culture every 10 minutes, which of the following equations best models the population P = P(t) of the bacteria culture, where t' is in hours? A. dP = 5P-1000 dt dP B. at dP C. dt dP D. dt E. dP at = 5P-6000 1.5P-6000 = 1.5P-1000 = -5P-1000