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MATH 151 Midterm: MATH 151 TAMU Y2014 2014c X3H Solutions

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turquoisegnu128

31 Jan 2019

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Texas A&M University

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Wed, 03/dec c(cid:13)2014 art belmonte: a bacteria culture grows exponentially. After 2 hours there are 400. (a) determine the population after t hours: we have y = y0ekt = 50ekt . Thus after two hours 400 = 50e2k, whence k = 1. Therefore y = 50 (8)t/2 or 50 (2)3t/2. Give exact and approximate times in hours: when there are 105 bacteria, 105 = 50 (8)t/2, which yields t = , approximately 7. 31 hr: if g is the inverse function of f (x) = ln x + tan 1 x, 4(cid:17) : observe that f (1) = . 4 , whence g(cid:0) f (cid:0)g(cid:0) . 1+x2(cid:17)(cid:12)(cid:12)(cid:12)x=1 (cid:16) 1 r (t) =(cid:2) 4 cosht 3 sinht (cid:3). x + 1. Identify the curve. (you can graph it. : now(cid:2) x. Recall the moahti, then follow your nose. y (cid:3) =(cid:2) 4 cosht 3 sinht (cid:3). cosh2 t sinh2 t = 1.

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