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A portion of the direction field for the differential equation A portion of the direction field for the differential equation = f(y) is shown below: The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the behavior as t \rightarrow \infty of the solution y(t) of the differential equation corresponding to each initial condition . = f(y) is shown below: A portion of the direction field for the differential equation = f(y) is shown below: The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the behavior as t \rightarrow \infty of the solution y(t) of the differential equation corresponding to each initial condition . The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the behavior as t →\rightarrow ∞\infty of the solution y(t) of the differential equation corresponding to each initial condition A portion of the direction field for the differential equation = f(y) is shown below: The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the behavior as t \rightarrow \infty of the solution y(t) of the differential equation corresponding to each initial condition . . A portion of the direction field for the differential equation = f(y) is shown below: The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the behavior as t \rightarrow \infty of the solution y(t) of the differential equation corresponding to each initial condition .

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A pond initially contains 70,000 gallons of water and an unknown amount of pesticide. Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons per hour. The mixture flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.Which of these is the general solution of the differential equation for the amount of pesticide, P(t) , in the pond at any time t?


A) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide. Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons per hour. The mixture flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.Which of these is the general solution of the differential equation for the amount of pesticide, P(t) , in the pond at any time t? A) B) C) D)
B) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide. Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons per hour. The mixture flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.Which of these is the general solution of the differential equation for the amount of pesticide, P(t) , in the pond at any time t? A) B) C) D)
C) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide. Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons per hour. The mixture flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.Which of these is the general solution of the differential equation for the amount of pesticide, P(t) , in the pond at any time t? A) B) C) D)
D) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide. Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons per hour. The mixture flows out of the pond at the same rate, so the amount of water in the pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.Which of these is the general solution of the differential equation for the amount of pesticide, P(t) , in the pond at any time t? A) B) C) D)

E) A) and D)
F) B) and C)

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An antibiotic is being administered intravenously to a patient. Fluid containing 8.0 mg/Cm3 of the antibiotic enters the patient's bloodstream at a rate of 100 Cm3/hour. The antibiotic is absorbed by the body or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.6 per hour. Assume the antibiotic is always uniformly distributed throughout the bloodstream.How much of the antibiotic is present in the bloodstream after a very long time? Round your answer to the nearest hundredth of a milligram.

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Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature) . Suppose the ambient temperature is 72°F and the rate constant is 0.1 per minute.Suppose the temperature of the object is initially 107°F. What is the solution to the initial-value problem comprised of the differential equation for the temperature of the object, T(t) , at any time t and the initial condition T(0) = 107?


A) Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature) . Suppose the ambient temperature is 72°F and the rate constant is 0.1 per minute.Suppose the temperature of the object is initially 107°F. What is the solution to the initial-value problem comprised of the differential equation for the temperature of the object, T(t) , at any time t and the initial condition T(0) = 107? A) B) C) D) E)
B) Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature) . Suppose the ambient temperature is 72°F and the rate constant is 0.1 per minute.Suppose the temperature of the object is initially 107°F. What is the solution to the initial-value problem comprised of the differential equation for the temperature of the object, T(t) , at any time t and the initial condition T(0) = 107? A) B) C) D) E)
C) Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature) . Suppose the ambient temperature is 72°F and the rate constant is 0.1 per minute.Suppose the temperature of the object is initially 107°F. What is the solution to the initial-value problem comprised of the differential equation for the temperature of the object, T(t) , at any time t and the initial condition T(0) = 107? A) B) C) D) E)
D) Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature) . Suppose the ambient temperature is 72°F and the rate constant is 0.1 per minute.Suppose the temperature of the object is initially 107°F. What is the solution to the initial-value problem comprised of the differential equation for the temperature of the object, T(t) , at any time t and the initial condition T(0) = 107? A) B) C) D) E)
E) Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature) . Suppose the ambient temperature is 72°F and the rate constant is 0.1 per minute.Suppose the temperature of the object is initially 107°F. What is the solution to the initial-value problem comprised of the differential equation for the temperature of the object, T(t) , at any time t and the initial condition T(0) = 107? A) B) C) D) E)

F) None of the above
G) B) and C)

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Which of the following pairs of values of A and B are such that all solutions of the differential equation Which of the following pairs of values of A and B are such that all solutions of the differential equation = Ay + B diverge away from the line y = 10 as t \rightarrow \infty ? Select all that apply. A) A = -2, B = 20 B) A = 3, B = -30 C) A = 1, B = -10 D) A = -1, B = 10 E) A = -2, B = -20 F) A = 10, B = -1 G) A = 2, B = -20 = Ay + B diverge away from the line y = 10 as t →\rightarrow ∞\infty ? Select all that apply.


A) A = -2, B = 20
B) A = 3, B = -30
C) A = 1, B = -10
D) A = -1, B = 10
E) A = -2, B = -20
F) A = 10, B = -1
G) A = 2, B = -20

H) C) and E)
I) A) and E)

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Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (typically the ambient temperature). Suppose the ambient temperature is 72°F and the rate constant is 0.12 per minute.Suppose the temperature of the object is initially 97°F. Given the initial condition T(0) = 97, how many minutes does it take the object to reach a temperature of 80.3°F? Round your answer to the nearest tenth of a minute.

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For each of the following ordinary differential equations, identify the order and indicate whether it is linear or nonlinear. For each of the following ordinary differential equations, identify the order and indicate whether it is linear or nonlinear.

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Eight differential equations and four slope fields are given below. Eight differential equations and four slope fields are given below. Determine the differential equation that corresponds to each slope field. Fill in the correct letter next to each number below: Determine the differential equation that corresponds to each slope field. Fill in the correct letter next to each number below: Eight differential equations and four slope fields are given below. Determine the differential equation that corresponds to each slope field. Fill in the correct letter next to each number below:

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