w2r - Write an integral that gives the total amount of...

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Douglass Houghton Workshop, Section 2, Thu 12/8/11 Eric and the Crowd 1. As Eric works out in the CCRB, a crowd begins to form to watch him. In the beginning, it’s just one person, but thereafter the rate at which people arrive is . 12 times the number of people already there. So if N ( t ) is size of the crowd at time t , N (0) = 1 and N ( t ) = . 12 N ( t ) . (It’s OK for N to be a fraction, because sometimes people’s attention is divided.) (a) Can you Fnd a function N which matches those criteria? (b) The total amount of attention Eric receives is given in units of “person minutes”.
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Unformatted text preview: Write an integral that gives the total amount of attention Eric receives during the 20 minute workout. (c) Approximate the total attention using a left-hand sum and a right-hand sum, with 4 subintervals. (d) Average them to get the trapezoid sum. What can you say about which of your three approximations are underestimates, which are overestimates, and how do you know? (e) ±ind the exact amount of attention using the ±undamental Theorem of Calculus....
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