17 RE 1.1.10 Problem 1017. A pond initially contains 1,000,000 gal of water and an unknownamount of an undesirable chemical. Water containing 0.01 grams ofthis chemical per gallon flows into the pond at a rate of 300 gal/h. Themixture flows out at the same rate, so the amount of water in the pondremains constant. Assume that the chemical is uniformly distributedthroughout the pond.a. Write a differential equation for the amount of chemical inthe pond at any time.b. How much of the chemical will be in the pond after a verylong time? Does this limiting amount depend on the amount thatwas present initially?c. Write a differential equation for the concentration of thechemical in the pond at time t. Hint: The concentration isc = a/v = a(t)/106.18. A spherical raindrop evaporates at a rate proportional to itssurface area. Write a differential equation for the volume of theraindrop as a function of time.19. Newton's law of cooling states that the temperature of anobject changes at a rate proportional to the difference between thetemperature of the object itself and the temperature of its surroundings(the ambient air temperature in most cases). Suppose that the ambienttemperature is 70°F and that the rate constant is 0.05 (min)-¹. Write adifferential equation for the temperature of the object at any time. Notethat the differential equation is the same whether the temperature ofthe object is above or below the ambient temperature.1.2ForthatIn the preceding section we derived the differential equationsIn egivebehof yof thcanGGGGD2 SeeAeroMoniSolutions of Some Differentia

dQ /dt=(rate in) - (rate out) The Rate of Change, is defined as Q(t)=[(flow rate of the liquid…

17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/ 106.

17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/ 106.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section17.2: What Is A Markov Chain?

Problem 4P

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