Pollution begins to enter 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   What is the amount of pollution in the lake after 22 hours, in gallons? Do not round until the final answer. Then round to the nearest hundredth as needed.

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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: World consumption of a certain metal is running at the rate of 328e0.02t thousand metric tons per…

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

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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.