r a lake at time t = 0 at a rate​ ( in gallons per​ hour ) given by the formula f ( t ) ​, where t is the time​ ( in hours ). At the same​ time, a pollution filter begins to remove the pollution at a rate g ( t ) as long as the pollution remains in the lake.   f ( t ) = 11 ( 1 − e − 0.5t ) ​, g ( t ) = 0.5t   How much pollution is in the lake after 13 ​hours, in gallons, rounded to the nearest hundredth?

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Q: A tank contains 70 kg of salt and 2000 L of water. A solution of a concentration 0.0175 kg of salt…

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Q: A tank contains 200 liters of fluid in which 30 grams of salt have been dissolved. A brine…

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Q: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure  water is then…

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A:

Q: The daily world production of oil can be modelled using 3 +100( -50 30 V = 10+100 30 where Vis…

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Q: A tank contains 200 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A: Introduction: A differential equation is one in which at least one unknown function's derivative,…

Q: A tank contains 200 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A: Introduction: A differential equation is one in which at least one unknown function's derivative,…

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

A: Let's find.

Q: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A:

Q: Pollution begins to enter a lake at time t = 0 at a rate (in gallons per hour) given by the formula…

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Q: 8. A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached…

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Q: Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially, there…

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Q: A tank contains 300 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram…

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Q: (a) A sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain…

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Q: A tank contains 300 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram…

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Q: 2Drug injection. Find and solve the model for drug injection into the bloodstream if, beginning at t…

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Q: 5. At any time t > 0, in hours, the rate of growth of a population of bacteria is given by dy dt y.…

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Q: A fish tank initially contains 10 liters of pure water. Brine of constant, but unknown,…

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Q: A tank contains 50 liters of water in which 10 grams of salt is dissolved. Brine containing 2 gram…

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Q: A tank initially contains 200 liters of pure water , starting at time t=0 The mixture in which 80…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.