exam1bsol - Math 16B (Fall..2009) Kouba C002) Exam 1 I...

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Unformatted text preview: Math 16B (Fall..2009) Kouba C002) Exam 1 I Please PRINT your name here : _____________ Egg"! ______________________________ -_ Your Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO TAKE AN EXAM FOR ANOTHER PERSON. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive little or no credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 6 pages, including the cover page. 6. Include units on answers where units are appropriate. 7. You have until 4:00 p.m. sharp to finish the exam. 1.) (2 pts. each) Determine whether each statement is true (T) or false Then Circle the appropriate response. Assume that a; and y are psoitive numbers. a.) lnm-lny=lnx+lny T 63 b.) lnx—lnyzi—E—E T @ c.)ln(m—y)=lnm—lny T ® d.) (lnm)y=ylnm T 6‘) 2.) (8 pts.) Chromium—51 is a radioactive isotope, which is used in the diagnosis of gastrointestinal bleeding. It’s half—life is about 27.8 days. If a sample of Cr-51 has an initial mass of 50 mg., how much will remain after 75 days ? W A: CfiKf—v 4:500K‘6W a7.‘i(< f=a7.8W/A:a5’mg ~> a5“: 5’0 3 I —~ ’1': Calgkfl 1/4041]: 017-?K" k: -—a .1 MC/ ‘6 9x15} Atb’oe m W» exacts,”— A:b"o€ 2.7.5; 3.) A pumpkin is dropped from a helicopter hovering at 800 ft. above the ground. Assume that the acceleration due to gravity is —32 ft. / sec.2 . a.) (4 pts.) Derive formulas for the velocity and height (above the ground) of the doomed pumpkin. slice): —‘ A ~ 7L Q 6910/ 5'20.» 0: O+C- C30)“ S‘Cf :‘352‘6 —% QT/QféQ-FQ fZO/SZ?OO——>XOOZO+C—§C':ZOO] "a =~léa~e +8300 (2 p s.) In how many seconds will the pumpkin strike the ground ? M -_ scejzo—g ~16£R+Eoo=© % (Qt—4:806 % {a‘zflfi {rt/37x71m. c.) (2 pts.) What is the pumpkin’s velocity as it strikes the ground ? 51135]: ~ 3m?) a: “Q26. 3 ref/M, 4-) (7 pts.) Solve the following equation for t : (In t)2 — 4lnt — 5 z 0 CM-E~5)</QM‘€+12:O afif35flflqf:,/ ,—§ f36§cfl 6.) (9 pts.) Let f(z:) = x2e”: , Set up a Sign chart for the second derivative, f”(a:), to determine any inflection points for the graph of f . __ - ~>< L 412%): fie/K6124. aX-e X : Xe Q’z—x) 2—» ‘ JIM/L2,) ~X 4%1‘CX)=G]€X(2«X)+ x- C Yam”; + xe {—1) : 6.x [R’X f XCQVX)*K j C CflgCQ—ngxi-xix] 7- C’XCXin-F (EL/3:0 A KA"{)H_& : O —-—+ (WY/i W" (MW ~ ‘12?“ : Qifi xv a0) ‘ V 9x 9\ 7.) (7 pts.) You deposit $1000 in a savings account earning an annual interest rate of 3.75% compounded monthly. How long will it take for your account to double in size ? . '6 A: Pfll+fifl)m+——s 74: [000 0-4—0 01:75, (a . . / V/4:9\000/AMM ‘6? 71%”; 0.0375— «as 00379 ’2‘ 02mm : (000 0+ (1 j _.* 01:04. (a 1/: "Vfl’WQZJM (LLm—J'L tiafiflfia+w 12L (,1 - ,QMQJrocB'w‘ AFT? (30/7/14- d 8.) (8 pts.) Use implicit differentiation to determine 3/ = —y for y4 + 3“: = (I: lny . dcc we w3-y’+ 3%» 3 : x-yLv'wL (MW 9.) (7 pts.) Determine if the following antiderivative is true (T) or false Give sup- porting steps or reasons for your answer. /(11;::)2dm ‘” +0 T/(Of: :1~l-:c2 A. - CWKVWVXCQX \ l+x9‘-— ma W799“. LMX’W ' 0967‘ lvxl Wk 10.) (8 pts. each) Determine the following antiderivatives. b 3 /A ti M:i awzévfl—VLQ 5&0? {Se 0 3/01 __ "I '3 l—E‘ (3%“42 1L c, D d.) /(at:sec2$+tancz:)-(anti-an)4 d3: f : X "—7 M:(XA’°<>X+ me/y‘kj ‘4 5 5 I; t J_ S“ 5%+Q/ EXTRA CREDIT PROBLEM— The following problem is worth 10 points. This problem is OPTIONAL. 1.) Solve /w4(x5 + 2)1/3 (ix by using the u—substitution u = (x5 + 2)1/3 . ~ 5 (/3 D -1 5’ ‘< (M UK—CK +01) HAM»3’Q(+;y5<J7K aiw: { quly 5 git—01):? l q Mun M' x. a ~— ~ I 2 5 [mm __.5 lot“: i— quy 5 w?“ v» QMD‘M: qu) 5' l5u-MQM 5 3 3 *8“ M 5 q : 1 Lu 4— Q. L, ...
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exam1bsol - Math 16B (Fall..2009) Kouba C002) Exam 1 I...

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