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How to solve an integral by parts?

How would you solve the mathematics word problem below on ALL parts?

  • Rumors are spreading that all the still standing Republicans trying the GOP are going to debate in Cornwall. The ton's 1400 residents have heard the rumor is given by P where P(d)=1400-1400e^-.16d where d is the number of days since the rumor first broke 3 days ago. a.)How many people know about the rumor now? b.)When will 900 people know about the rumor? c.)How many will know about the rumor in another week? d.)Draw graph of P.

  • Answer:

    This is a logistic. a) if d = 3, then we are at today P(3) = 534 b) p(d) = 900 = 1400-1400e^-.16d Solving for d we get 6.44 days, so that will be 3.44 days from now c) d = 10, so P(10) = 1117 This is a graph that starts at (0, 0), climbs steeply til the tenth day at (10, 1117), and then curves to an asymptote at 1400, which it never really reaches, but includes (20, 1343)

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OK mur.... P(d) = 1400 -1400e^-0.16*d. a. substitute in 3 for d and you should get 534 (rounded) people know about it now. b. When will 900 people know about it? 900 = 1400(1-e^-0.16*d). divide both sides by 1400 and then subtract 1 from both sides leaving -0.357142857 = -e^-0.16*d. Now multiply both sides by -1 to make both positive and then take ln's of both sides to get -1.029619417 = -0.16*d. Now divide both sides by -0.16 and you get 6.44 days rounded. c. Add 7 to the answer in b and then multiply by -0.16 to get -13.44 for d then do the math to get 1237 (rounded) folks will know. d. Can't graph in this post.

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