4"< k _ Math 2123 Spring 2010 Exam II FORM A Name:' Section _:..; ' id#: Instructor: --- _ " d, - ii. /'" Read all questions ciirefully and answer the

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13 4"< k _ Math 2123 Spring 2010 Exam II FORM A Name:' Section _:..; ' id#: Instructor: --- _ " d, - ii. /'" Read all questions ciirefully and answer them Clearlyand completely. Show appropriatework to receive maximum credit. In parl.icular,show all definite integrals whenever necessary. If you can label an answer with units you should label it with units. Round model eoeffieients to the thousandths place, and round numerical answers to the hundredths place, unless the [ directions for the problem specify otherwise: YOUwill have 75 minutes for the exam and point Valuesareas indicated,..,... _, 1. Find the generalanliderivatives: "'D_ - " ' _,e " ' _ " ) [( 6 =') '_'[--_1 (J'z'_- _,,x/ =3."i "{ " -- _'-- a. jx t._-+e ]dx " "Y_.)/'"_'_)_ ""_J_'_' (9p'oints) t,$' '17_(_"_ ( r..,=+_:2r<--0'-- "_U' " _.c\<3:'l':._../7 :_4 _ l_f. <0 :' 4c " b ff 519 dx (6points) "-7x' 14_x, " ".U )<,ITS'/') ' ":.. I '* : t 6%" ', [. %

14 2. An omithologist determines that the body temperature of a certain species of bird at various times is in the following table. (12 poij ts) i Time 8a.m. 9a.m. 10a.m. II a.m. 12noon 1 p.m. Temperature (de_rees,.gelglus'_ "x a. Genera_bic model for the data, aligning 8 a.m. with an input of zero. X b. Findt_:averagevaluenfthebird'sbodytemperaturebetween9:15amandll:45am.._ [ q:ts- tis/v'x _ l[:45ouv, [L4. o_r_<_%_. Z_ )t;_ O,.S-. 00_. _.0X3.13qx_ 40._OB 3. Evaluate [ 0" ( (11 points)._.)

15 \,.. < A small business that produces popular appjets for the Android ph0ne ha_smonthly... revenue of $5_t_ring its first year in business. Google is considering purchasing the.. company, (v-_oserevenue Google prbjects will increase byt_.8%o [6er_ ear. Google assumes it can obtain a 10.7% rate of return and decides it will offer to purchase the., c,4 company for-the 8-year present value of their revenue, as a continuous mcofne stream. a. Wnte tile flow ra_r(t); _C, _ "" "(13 points) b. Find the _nount of Google's offer. 5. In an effoi-t to solve the probiefia of high textbook p_ces, Sani started an Online service to help people buy and sell used textbooks here at OU. Sam's currentannual profit is,. _ and be expects it to remain'constant. Sam has found an account that earns 8.5% APRcompounded continuously and begins investing 38% ofh!s profits into the accoufit. o asa continuous income stream. Sam w_ld like to use,this investment to purchase a...- house in i 4 years. How much mon_4vil! he laave? (9 points) _ ,:- <-.O... fi_v ' - _ "" / N.... z L

16 6. The demand for oranges is given by D(p) = -0.05p p thousand bags when the price is p dollars per bag. The quantity of oranges supplied by producers at a market price ofp dollars per bag is given by r0 thousand bags if p < 1.6 ) S(p) p 2-0.I 23p thousand bags if p > 1.6 (22 points) a. Find the total amount consumers.ar/willing I J and able to spend for.9501b_s of oranges. _:.ss G ip3_p>.sr b. Find the producers' surplus when bags of o ges are $4i2_eacb. c. Find the Social Gain at the equilibrium price. e_ ( s._a, s.ot) 7 59-X..q, v. v,--" uls 0@34{)z;E.l_

17 _s.s,. 7, t, i : Oc_ " Please round answers to the nearest thousandth on problems 7-9., [12- x. " ' - " 7. Given the functii3n f(x) otherwiseif 0'_<x _<12. answer the following: / (9 points) a. Use _e definition Ofprobability d ensity function io show that f(x) is _av_lid _/_,. (!:_C_)d_--/ _.._._.!_-,sw _-_,_.. Pf" ' " 8. The lifespan 0f an apple tree is exponentially distributed with an average lifesp_in of i_ e sketch of the pdf and shade the region correslsonding to the p"rol_abili@you are finding. X.Z, ],, --_ - i 'K_, -K,._: ;y,_ (", "-,, t,.;,b,-_ -_, - -2"-,'-,.1. _ (7 points) _.../ 37 years. What is the probability _ that _mapple kk_'_k./, tree will live t\ at most _"750 years.9 "Draw a 2_ //l/ :- 9. An internet service provider offers broadband access which is normally distributed with a mean download speed-of F.8 megabytes persecond, and a standard deviation of 0.26 megabytes per second... _ --- (/1points)" "; a. The probability that a dow_oad Speed is bct_:_en 0185 and 1.72 megabytes per second (_,_,_!,_os_t _? a(, - novnxx\96 C._i._.,t_'l. 0_ -_ - '_ J 17_.,_,7_7fl I. _(s_5_-:-"st?.o.p zl = is_, "_a" The-f --_pr babiiity thata downloadspeedisatleast 1.66(_( " m.egabytes(o(o ) per"second( '":_- '.(o(_)._ - a_ 10f.(011,% _,.i _,.,. 0

18 o _.Math ' " _ Exam IH FORMA id_i Instructor: Read all questions carefully and answer them clearly and completely Show appropriate, work to receive maximum credit. If you can label an answer with units you shoum label it with units. Round model coefficients to the thousandths place, and round numerical answers to the hundredths place, unless the directions of the problem indicate otherwise, You will have 90 minutes for the exam and point values are as indicated. 1. Given the function D(h, k) = kaf_ 7:6-9.8hk, sketch the 150 and 250 contours for 5 _<k < 25. Be sure to label the axes and the contours (11 points) _c_,_) _@_7_- _._, O - _, o_.._n K.. f,q.g_ _V'-.-},<---"

19 2. The table below shows the demand for air travel between the US and Europe when g is the US gross national product and p is the price ofa rounod.ttip-ticxet..._ 13 points) _.,,_ soo looo uoo_, 12o0 L/ /1400 t [ t l / j 7152 a._-fin_dan appropriate complete quadratic cross-sectional model for dem_ for air travel between$1100./the US and Europe when the US GNP is $1800 billiont.//and the ticket priceis _ l_0f_.a_--_,_. ) b. Use your model to approximate the demand for air travel between the US and Europe. when the US GNP is $1800 billion and the ticket price is $1100. " ' 3. Find all first_order partial derivatives of h(x, y,z) = 0.237x+,o zs. in y (3 ] xy (19 points)/ You do not need to simplify yourfswers. / t// _/ - y _rloa) "_/7. I(] - gz.la'/

20 >,J,.' 4. Suppose P(I, S) gives the monthly profit of a furniture store in dollars when they carry I million doll,ars of inventory and have S thousand square feet of floor space available. : " (! 5 points) a. Write a complete interpretation of P(5, 150) = :.. ' - dt_/t_tb f_f_d _-he,.5-_owj_0,si_bk_gdso_d.,,.- _ :_.,. ;..,jo%_ -,, b. Writea complete interpretation of t:3p "? , _., doilaf(_o_ i.. t_. c. SuppbsePs(3.3, 200) = 525. The units for 525 are _{_t/(-_ b k. (Do not give a complete interpretation, just give the units for the specified number only.) I1,

21 _-,x,/<_ts_5-t, q - I. f6n_k-3hu -Iv_ L_,.-do3fnc%_rS_(-_ 5. The price of land within the financial district ota city is approximated by the model L(w, n) = n n _ n w w dollars per square foot, when the property is located w miles west and n miles north of the municipal courthouse. Miles east or south of the courthouse are given by negative w or n values respectively. Find and clearly classify all critical_. nts_ofl-- Please state your answer(s) as ordered triples _ label all answers _riate units..). z, f-i,-'l_f -.i_- (2-_point_) L Lw_n} -7. _.oo _x -ts.t_ - _.sq_ z

22 q /,, 6. A local liquor store sells two expensive brands of white wine, one from Ge/-many and the other from It.aly. The Germanwine comes in cases of 6 bottles and th e German wine comes in cases of 8 bottles. A model for the total number of cases of both Wines is given 1 1 by C(x, y) = -6x +_y cases, where x is the number of bottles of German wine and y is the number of bottles of Italian wine. The annual profit from the sale of these two wines can be modeled by P(x, y) = x y xy x y 2dollars, with x and y.asabove. Suppose the stoic has limited storage space for these two wines and can only store 100 cases total...,.. (19 points) a. Find the maximum annual profit under the gwen storage constraint. Include all, _ decimal accuracy _ivdn on your calculator or state your answer in fraction form _.v. L _.,o. f.-5u._4b/ h I b. Use close poin.ts to Show that you_ answer to part (a) is a constrained maximum Include all decimal accuracy given on your calculator or use fractions in your close point analysis. x-,s/,,,..- %,_... ". '_ xc._,..._. NL (% m

23 _,_ 10.3 r_4 IO,q el. I I0_,1