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Unformatted text preview: ortional to the amount of water present. (b) if the water drains off at a rate that is proportional to the product of the time elapsed and the amount of water present. 42. At a certain moment a 100gallon mixing tank is full of brine containing 0.25 pounds of salt per gallon. Find the amount of salt present t minutes later if the brine is being continuously drawn off at the rate of 3 gallons per minute and replaced by brine containing 0.2 pounds of salt per gallon. 43. An advertising company is trying to expose a new product to a certain metropolitan area by advertising on television. 504 CHAPTER 8 TECHNIQUES OF INTEGRATION Suppose that the exposure to new people is proportional to the number of people who have not seen the product out of a total population of M viewers. Let P (t ) denote the number of viewers who have been exposed to the product at time t . The company has determined that no one was aware of the product at the start of the campaign [P (0) = 0] and that 30% of the viewers were aware of the product afte...
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 Spring '10
 SMITH

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