Solve the elementary applications of Differential equation: 1. Suppose that the quantity of a radioactive substance originally weighing Xo grams decomposes at a rate proportional to the amount present and the original quantity is left quantity is left after 1000 years is halved, find the time when the a

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Q: Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where…

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Q: 4: A radioactive substance decomposes at a rate proportional to the amount present. If one-half of…

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Q: Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt…

A: Thus, we need to find  and  first.Here,         (concentration of salt in inflow).(input rate of…

Q: Use the Intermediate Value Theorem to show that the equation • (c) V(t) = 2 has a solution for 0 < t…

A: The given equation is, V(t)=-t2e-t-2e-t+3 The intervals are (0,2) c) Now, we have to find t value…

Q: Let Q be the amount in a mutual fund earning interest for t years at an annual interest rate of r,…

A: Consider the equation

Q: Solve the problem. A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved.…

A: Step:-1 Let x be the quantity of salt in lb, dissolved in brine at time t. Now, Given that initially…

Q: Suppose we have a tank that initially contains 10 litres of brine in which there is dissolved 1 kg…

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Q: A discharged capacitor C = 2700F is connected in a series with the resistor R = 10. (a) Find the…

A: The differential equation that governs the voltage drop on the capacitor in the circuit is given by…

Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

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Q: 2. In a certain culture of bacteria, the rate of increase is proportional to the number present. If…

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Q: The amount y of the drug Warfarin in a patient’s body after t hours satisfies the differential…

A: We have to find the time and the rate of dissipation of the drug increase or decrease.

Q: . One model used in medicine is that the rate of growth of a tumor is proportional to the size of…

A: Given:The rate of growth of a tumor is proportional to the size of the tumor.To Find:a) The…

Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: a) Given half life= 58 minutes  So if initial value= C= 1 Then after 58 minutes A= 1/2=0.5 Using…

Q: Select the third differential equation, dy=-x2+y+0.5, and set the initial values to xo = -2.1, Y0 =…

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Q: To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t)…

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Q: Assume that the number of people y(t) (in million) who have heard the President announcement  to…

A: Given the differential equation :

Q: Isaac Newton observed that the temperature (in degrees Fahrenheit) of his morning brew (F) changes…

A: Part (a):   According to the question the temperature change of the coffee is directly proportion to…

Q: Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both…

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Q: Suppose your bank offers 3% continual annual interest on the balance of your cer- tificate of…

A: Given, B(t)=balance at time t and , annual withdrawal of $300 Considering the interest , we know…

Q: Suppose that a large mixing tank initially holds 900 gallons of water in which 50 pounds of salt…

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Q: Let y(t) be the size of a colony of bacteria after t hours. Suppose the rate of growth of the colony…

A: We will find out the required solution

Q: A certain virus is known to spread among a population at a rate proportional to the fraction of the…

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Q: Von Bertalanffy's equation states that the rate of growth in length of an individual fish is…

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Q: iters of brin ing, flows or

A: Given as, The tank contain=400liters brine holding=100kg water containing=125kg The tank at the…

Q: In the logistic model for population growth, dP dt P (12 - 2P) where P is population and t is time.…

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Q: A tank initially contains 17 pounds of salt dissolved in 450 gallons of water. Starting at to = 0,…

A: According to the given information, For part (a) Tank initially contains 17 pounds of salt that is…

Q: The initial concentration of phosphorous (C) in a waste water pond is 10' ppm, as against he…

A: we have dCdt+0.06C=0, C0=107 ppm we know that by Euler's method  yn+1=yn+hftn,yn where tn+1=tn+h we…