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# pracexam1bsol - Math 16B(Winter 2008 Kouba Exam 1 Please...

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Unformatted text preview: Math 16B (Winter 2008) Kouba Exam 1 Please PRINT your name here : ______________ KéLI _______________________________ 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 pagcs, including the cover page. 6. Include units on answers Where units are appropriate. 7. You have until 8:50 am. sharp to ﬁnish the exam. 1.) (2 pts. each) Determine whether each statement is true (T) or false (F). Then circle ,9. the appropriate response. Assume that :1; and y are psoitive numbers. a.) 1111: + ln-y =1n(;r + y) T ® b.) 6"" + 6y 2 (6’)” T a c.) 11113 - lny = ln(;ry) T @ 2.) (8 pts.) Cesium-137 is an isotope produced by nuclear ﬁssion, and is used in medical radiation therapy devices for treating cancer. It’s half—life is about 30.17 years. If a sample of Cs— 137 has an initial mass of 100 mg, how much will remain after 100 years ? W A: Cer’ C:l&°”7_:——BA 1006: ) Q {—3017/74'4A16’0/V7 -—=0 0,0: 1006.30.1—7K 3° (7K jMQVA) __=, _L z 42, ~.~, ﬁne/a] t. 30.17K "" k : 30. I“? a 3‘ MCI/3.24, 140210“) .4” A: '00 € 36- to ~ MtZ/OOW --—"9 A: (00 C 30'17 810.017.— L_‘_’__.___———n j ' Ag? 3.) A watermelon is dropped from a helicopter hovering at 1600 ft. above the ground. Assume that the acceleration due to gravity is —32 ft./see.2 a.) (4 pts.) Derive formulas for the velocity and height (above the ground) of the doomed watermelon O:O+C~—7 Q:o —-r g“ 5C9): “/6‘6’14- C, (+36 8:1600) -——¥ ((300 : 04. c—vct Igoo ”" 1.5%" (3&2: léOfov lei—A) 2 pts.) )In how many seconds will the watermelon strike the ground .7 El< 1&3, ?M 366’ ~6 —» ((900‘—1é>‘69“ : 6 —-; my; two ~—> 1.3/00 -* c.) (2 pts.) What is the watermelon’s velocity as it strikes the ground ‘? F 5‘()o):"3o2(l6]: “320.1(35-/4J——c. 4.) (7 pts.) Find a function f (:L') which has the following properties : f”(:L') 2 20:53 + 2, VP f’(0) = -1, and f(1) = 3 I. ——=r 4900:: 5Xq+RX+C CXZOJ‘PG): -1] ——-> l f 4: “we a e: ~l A #QOtéx‘tI—RX-J g .msz xf+xi >< +6 (\$54—61): 3) A 5.) (6 pts.) Let y 21:311117 . Solve y’ = 0 for .17 . 2.7 y'; x3.%+3x’zﬂmx : X'z4— 39(12de *0 :X’L(l+3/¢‘4X)—-> 2;}{0 (No) 0»: 1+3LAX:0 ——> 3/74X:~( 2: ﬁx: _. 93—, 6.) (9 pts.) Let f(a;) = we” . Set up a Sign chart for the second derivative, f”(a:), to determine any inﬂection points for the graph of f . 2*: 41.00 : xex+ (CK 3» \$1100: xex+ hex +e’< 2‘- XQXJVRCX : EXCKJ—R): 0 ——=r 8%) (No) 04 X:”2 7.) (7 pts ) You deposit \$5000' in a savinos account earning an annual interest iate of 5. 5% f. compounded monthly. How long will it take for youi account to double 111 size .7 W A: (0017”)ch pcﬁiooc: V‘:o.ob’é; ) MCI; A:ﬁ'/0/006 -—§ / lék (0/ 000; 5000 ( 1+ [0 fl at 0 9705'; —% M <2: ﬂu (1+ 0 i : £44 .2 h" -E 3 055 x 102. (o 3 I .2 124 (1 +9.;__’—) ’7’”- I 9x 8.) (8 pts. ) Use implicit differentiation to determine 3/: % for 31: +1312 51‘: lny . X I 3x+Yzox’:ﬁv1Y——~ 3+ Y"5’%«5+aw'5 ::((-'Y l Y I? X a \r (Hf—~39]: ~3~Y 5 Mb“ I ”3*7258/“45’ -—3 Y ~— X I/ 017’5 -— \/ 9.) (7 pts.) Determine if the following antiderivative is true (T) or false (F). Give sup— porting steps or reasons for your answer. ) 0+><°l (1 ~ X RX I XX 11x 0+9“) ’\ ((+ka 10.) (8 pts. each) Determine the following antiderivatives. a.)/m(3+¢3)dm 2 5<sx¢><jﬁjkv 57 .. °2 oz ‘§K+~?X +Q, -ig’jF—q ~ 1 ,1 341 5 V5 Md‘ch—"E’H- +C, 3/ - g; <71 - (5(5<+3</j 4—Q d.) /(J:secg.z:+‘ran;lt) - (mt-(111.102 (11' CM H 1' X MK ﬁ AM :CXMRX+ MK) M) 3 : SMQJM;§LH3+C,: SQQWMK) +0, EXTRA CREDIT PROBLEM The following problem is worth 10 points. This problem is OPTIONAL. 1.) A parachutist jumps from a plane at an altitude of 2000 feet and free falls for 10 seconds. At that point the parachute opens and the the paraehutist ﬂoats to earth at a constant rate of 10 ft. / see. From the moment the parachutist jumps from the plane, how much time will it take to reach the ground 7 l ﬂ 5”L+/:~32’*5C+/:~3275»> 5W: ~ @914. X000 g j / :: ~ 6 O : 4°C SCO/ / (Mo/7L gmp \$25) ...
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