1 Point Consider The Mixing Process Shown In The Figure A Mixing Chamber Initially Contains 3 Liters Of A Clear Liqui 1 (90.03 KiB) Viewed 61 times
(1 point) Consider the mixing process shown in the figure. A mixing chamber initially contains 3 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.75 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well- stirred mixture is pumped from the chamber at a rate of 10+ r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dQ dt 0.75r-Q/3(10+r) kg / min (b) The objective is to obtain a dye concentration in the outflow mixture of 0.5 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? r = 3 L/min Would this equilibrium value of r be different if the fluid in the chamber at time t = 0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it take for the outflow concentration to rise to within 1% of the desired concentration of 0.5 kilograms per liter? t = min
(1 point) A population of squirrels lives in a forest with a carrying capacity of 2100. Assume logistic growth with growth constant k = = 1 yr-¹. (a) Find a formula for the squirrel population P(t), assuming an initial population of 525 squirrels. P(t) = 2100/(1+3e**(-t)) (b) How long will it take for the squirrel population to double? doubling time~ years
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