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# exm1 - What is the number of bacteria after 5 hours I...

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Name (please print): January 31, 2008 ENGR 232: DYNAMIC ENGINEERING SYSTEMS I: EXAM 1 I Section No.: I Instructions: 1. Pleasewrite your name and section number in the space provided. 2. This exam is closed book and notes. 3. Calculators may be used. 4. Points will be deducted if the work is unclear and the answers are not justified. Evaluate the following integrals d v:;. e ?>X V ~ Je31-d~::;. 1. (4 points) J xe3xdx 2. (4 points) J 3xJ(1 + x2)dx ~) '1::: 3 j t '-cd ~ -- ~JtL-d-\. :"!3 t 5+ L - 3' _ ) - ( i ?J12- ::) ::r :: \...l.-t '(..1.. ) -t L ~ \; \J \k~?- ::: t ~ U~1\ 1..) 1- .-/) '-r ,,2 -_ t 'L -:::.j 2-xcl 'f.::' ~ td t ::::) X-cl "';. bdt- ~ (L -V E- Q.~ \oV'J ( B) J 1\ NSW ~ f.. \.:> Li (J-\-'f-.2-j3,2-Jr C - 6 --

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Name (please print): I u.boV) January 31, 2008 3. (5 points) The number of bacteria in a culture increases at a rate proportional to the number of bacteria present at any time. Initially the number of bacteria is 200. After 2 hours it is observed that there are 400 bacteria present.
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Unformatted text preview: What is the number of bacteria after 5 hours ? I ) . ) _ ) ~et-)<,:::tw. af-~C ft> I~ X (0")-- 1. ..00 XC '2. .):: 4 (:) t y ( S--) .11'))z.1 i-:::.) xCtJ ::- 2,-00 e-z: dV = _kV2j3 dt (a) The volume of a sphere is 47rr3, where r is the radius of the sphere. Find the differential equation 3 for the radius of the evaporating drop. (b) Find the formula for r(t), the radius of the drop as a function of time. V =4 Ii l' 3-) d"y:= Lt 1\ . :tY'Ld~ = 4 TI Y'"2-~--:r-d \:' 7 d:t-d t--"2-1 L. 2, ~ _ \L ( 4~ ) ~\[,) 3-\:.~l/3 yL (f) ~\\J'€N\: d~ :::_V_v'2. ./3 d-t-' 4 ~ d..2:':::-\c (Lt 11 ) '2/3 pX ell-' ~ .--'2.-----::::)\ d~ ~ _\c 141i ) 13 . \ <:::-¥-C dt l-'-~ Lti\-. (-t A"'-)""'CIV' (0. .) ~) \ d V' ::-\<:.c.Jd-\:;-_ \LC-t+ L , \Ae. .Y'( (-=-~\13 L t ~) 47\ (£:;> ~-k1. ",+---...
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