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Good morning answers user. I am working on this math (DifferentialEquations) homework. Please help me with the rest of thequestions I attached down below. Please work on it carefullyand make sure it is 100% right because it is worth manypoints. You do not have to show work just give me the rightanswer. I will upvote if I get it right and down vote if it isincorrect.
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(1 point) A tank contains 50 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. (a) What is the amount of salt in the tank initially? amount = 50 (kg) (b) Find the amount of salt in the tank after 4.5 hours. amount = 39.02 (kg) (c) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = 0 (kg/L)
(1 point) A tank contains 1220 L of pure water. Solution that contains 0.09 kg of sugar per liter enters the tank at the rate 9 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) = 0 (kg) (b) Find the amount of sugar after t minutes. y(t) = 61(1-e^(-9t/1220)) (kg) (c) As t becomes large, what value is y(t) approaching? In other words, calculate the following limit. lim y(t) = 70 t→∞ (kg)
A population of squirrels lives in a forest with a carrying capacity of 1100. Assume logistic growth with growth constant k = 0.8 yr¯¹. (a) Find a formula for the squirrel population P(t), assuming an initial population of 275 squirrels. P(t) = (b) How long will it take for the squirrel population to double? doubling time years