Good morning answers user. I am working on this math (DifferentialEquations) homework. Please help me with the rest of the questionsI attached down below. Please work on it carefully and make sure itis 100% right because it is worth many points. You do not have toshow work just give me the right answer. I will upvote if I get itright and down vote if it is incorrect.
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Thank you.
(1 point) A thermometer is taken from a room where the temperature is 22°C to the outdoors, where the temperature is -6°C. After one minute the thermometer reads 12°C. (a) What will the reading on the thermometer be after 4 more minutes? (b) When will the thermometer read -5°C? minutes after it was taken to the outdoors.
Sunset Lake is stocked with 1200 rainbow trout and after 1 year the population has grown to 3900. Assuming logistic growth with a carrying capacity of 12000, find the growth constant k, and determine when the population will increase to 6100. yr-1 k = The population will increase to 6100 after ~ years.
Consider the mixing process shown in the figure. A mixing chamber initially contains 4 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 = 0.75r-(10+r)*Q/(4) kg / min dt (b) The objective is to obtain a dye concentration in the outflow mixture of 0.6 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? r = 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 4 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 0.6 kilograms per liter? t = min unter