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1105P1sf11 - MACIIOS 024 027 Name K E 5 Project 1(circle...

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Unformatted text preview: MACIIOS 024 027 Name: K E 5 Project 1 (circle your section) due September 20, 2011 Please follow all directions carefully. Include as much relevant work as possible to ensure maximum credit. Where explanations are requested please write legibly and use complete sentences. (18 pts) 1. A checking account is opened and $600 is withdrawn every month. Assume this account earns no interest. a) Afier two months the value of the account is $8,400. Let t represent the number of months elapsed since the account was opened, and write a linear function V(t) = b + mt that computes the value of the account fi‘om the time it was opened until the time it becomes depleted. lo: lm‘liafi value. = $9400 ammo) =- 3‘46360 a) VG: 5 dMOO “600% m: slope = “$GOO/Mm-ila b) Complete the table and draw a relevant graph for this function. ' V ( o) = ‘1 600 Va) = euoe VCS) = 6600 v0o=3coo v05) : GOO VC-E) = o s; QQm—émkzo 600%— ‘ O‘WOC 'l‘«' 600 2 l6 manila s c) Let t 5‘ represent the number you entered above in the last row, first column. Explain what the statement V(t*) = 0 means in the context of this situation. ‘ VUG) =0 Wms lkqfia afier l6 menu 6.0L 4’43. W lots been, ' wilkdpaum rlirm vile, acanfir - d) What are the appropriate units for the slope of your linear equation? (no numbers, just units) ‘. . M1 M dwlollms er mmlla Slope bwvls - 'wpwl' (mt-ts “MM. Sel' builder e) Use “notation to describe the relevant domain and range of this function. _meuw= {4 l {= 0,1, 3,3 . ....) {9116} WWW Rm‘ {V [VT 0,600) 11:00,, I300}..‘.,)qoog awe? Range \hC mslhj - c Maw. 77 77 W“ (l2 pts) 2. The population of a country has beengmflgg‘between years 1990 and 2010, but the rate has every year. Let P represent this population as a function’ of time t. a) Draw a graph that could represent the general shape ofthe b) this ___owth attern is ex-ected ___u ,.__a_nt_u-__ _ g ange of P for the 20 graph of P. The graph is (circle one word From each line): the avenger .. . year period from 1990 to 2010 is used to predict the decreasing constant population in the year 2015, would this prediction be: linear (circle one): too low correct concave up . ‘ Explain the reasoning behind your choice. No calculations (— linear pmlh tit-imam necessary. ' ”’ir; act...) WWW); 1k». hum.” paint-ii... assumes \ Ox Cousin/wk increase. this popwlehw/ lowlr ll», rad-9.. 0‘? firm MS | . been decreasing wan M @Ndic‘l’imwwfiflbfldvobla‘n - (12 pts) 3. Draw an accurately shaped graph to represent each situation. In the answer blanks write down whether the graph is concave up, concave down, or neither. in each case the independent variable represents time. a) A car is driven with constant speed for 10 seconds. The dependent variable represents the speed of the car. \ Speed (concave up, down, or neither) a) [ l6, [JIM 1 ': lemalt 5M “9*; apeeQ Staph is. a. infirm/dag, like, time 0 ‘ 0 b) A car is driven with constant speed for 10 seconds. The dependent variable represents the distance traveled by the car. distance (concave up, down, or neither) b) h 8 )1 hi Cmsbwdl: speerfl a; mush/«k slaps. or? MWLQ graph $ dist-imm- tvlmawj at a, mic l0 CM! 0) A car is driven with increasing speed for 10 seconds. The dependent variable represents the distance traveled by the car. (concave up, down, or neither) fl) CMCM % lacuna/M5 speefié 4%. cm- cm distal/«Ace. a} a \Qtslu" moi-E. 6L9 H speak up g AiSVlWL-L 65mph ‘15 emcm osp- distance (18 pts) 4. The graph shown represents the average rate (AROC) at which the temperature changed during a 6-hour time period last week, beginning at noon. Each input 3: represents the one-hour period ending at hour it, and each corresponding output y represents the average rate at which the temperature changed during that hour in units of F° per hour. For example, the point at (l, 5) means that during the time period from noon to 1pm, the average rate at which the temperature changed was 5°F per hour, and the point at (5, -2) means that during the time period from 4pm to 5pm the AROC was —2°F per hour. thoi. the. tartar: 41‘“ (Maul iAorw it) M WWW rah has. hasi‘vmukfi of 4L1. . indoor (it) trivia/mm 4M. CWSQweQIALj WWQQ M MD. op ianiAoM- a) if it was 80° at noon, what temperature was it at 6pm? NOON . \ 9- 3 Li S (a 3) (3H 6 o o 0 o o a C30 :?%6 ?%5 "$861 fqo 3:9538 ngo b) At what specific time (noon, 1pm, 2pm, 3pm, 4pm, 5pm, or 6pm) was it warmest? see. ‘PW‘i‘ a) mm c) During which one-hour time period (noon-1, 1-2, 2-3, 3-4, 4-5, or 5-6) did the temperature increase at the slowest rate? IF?” 3PM“) LiPM 4i»; W’s-cram WA] . c) 3-H BE! ‘ . ‘ thmcmseai. hy 1°, d) During which one-hour time period (noon-1, 1-2, 2—3, 3—4, 4—5, or 5-6) was the temperature the same at the end as it was at the beginning? mi 5. pm M Wpemm was €50: d) “3pr B200. we ovi- a put to, lemma was 9hr eso. e) Draw a scatter plot for the temperature and connect successive dots with Temperature line segments. 40" 7. — A his M— (0,36% (1,86), (ass), 22 EWJH 3H“ (3ng3/ (Li lqo)/ (5%?) (6/ ‘8“) gao ' 60° 6 . . . h . . 9 PM i) What IS the relatlonship between the average rate of change for each hour and the slope of the lure segment connectrng the beginning and ending temperature point for that hour? Explain. "the {EEOC For each how:- is ogua'tvalew'i‘ it: it». sicpe of? a. Una sagmwi: CUMIAQCinIAS M [D limmu'xfi magi 0M9. Pot-Wt m 4%. iemwaiww. grapthw MA eariieuflar loam“. (20 pts) 5. Water is being heated until it boils (100°C ). The following table represents the temperature of the water t minutes after the heat was first turned on at noon, with C representing the temperature in degrees Celsius at time t. "m (159,-. (ms 4, (16,60) “ 1 b) What was the average rate at which the temperature rose per minute between 12:00 and i2:16 p111? (Include proper units.) a . b) 3 4mm. ..__—_-1-at '2; 32:“ '3‘ Par MinWi'Q [(0 1mm; town's 0 2 4 5 810121416 c) Enter this data' in L1 and L2 of you1 graphing caicuiator and use your calculator to construct a linear regtession for the t'ernpeiature of this water in terms of the number of minutes elapsed since noon. Express both the vertical intercept and slope with (m- ecimal place acouracyé‘ You: equation should be' m the form C: b + mt. I 3 L331; l G '. 0 no ow jg 7:6 lG ‘ d) At what rate does the calc1il>ator formula show the water is being heated? (Include proper units ) 3 O % 2 1M 13. z: ‘ d) ' ' e) Use the calculator’ s regression formula to pledict the temperature of the water at 12: 25 pm. Show work. '31:?) o: L|.O‘7+ 3.090.155: stow“ ammo— f) Use the calculator’s regression formula to predict the temperature of the water at 4:00 pm? How realistic is this answer? Jr u: 0 W833?“ Q 0 C. -‘- LI.O‘7 +36%(‘3L1031‘ ”13.91? D i: Ill-IO (This is empieieiri mumeiisvilc. (“'4 male: loads 01 km) at 100°- g) Use the calculator’s regression formula to predict the time of day (nearest minute) when the water will boil. 0.132% “5,031; -.~. 100 1c: 4533 g)_l9;i7>_ip_m_ “5.0 {:4qu 31°? . g 3 3 (“.15 imp/1136 h) Use set-buiider notation to indicate the relevant domain of this function. W iw M t t: 0 7 Domam:{t[os-Lt 31} movie! limits '- ‘L; 3i W—W_ 5 (20 pts) 6. You want to buy potato salad and cole slaw for a party, and have $45 to spend on these two items. Potato salad costs $2.25flb and cole slaw costs $2/lb. Let x represent the number of pounds of potato salad you buy, and y represent the number of pounds of cole slaw you buy. a) Write a linear equation (AX + By- = C) representing the possibility of finding containers of potato salad and cole slaw with a total cost that adds up to exactly $45. ' DJSX: mama, sprawl an Palate Salad 91”? MM Spawlr we Cole slaw b) It might not be possible to find containers of potato salad and cole slaw that add up to exactly $45, so realistically yOu will end up spending $45 or less. Change your equation to an inequality that represents this possibility. fl use 9 b) aasx +32 —’= 95 a) 9.35%? +2); =LIS’ C) Use set—builder notation and appropriate inequalities to express the sets of possible values for x and y. xx. 510 O 0 321.6 3y = HS=>y=eaJ5 1w a.a€x='vt$$ x=ao M (1) Use the axes below to shade the solution set to the system of inequalities created by parts b and e, Label all vertices of this region with appropriate coordinates. e) For each of the following points, determine whether they lie inside the shaded region, on a border line, or outside the shaded region? Show how you decide. 0 i) (10, 11.5) :.as(lo)ea(u,5) :H6.S >Lg5 i) owisiale . a) (s, 13) 3.35 (9)4 9.03) = uuz L16 firimtde t) In the context of this situation, explain what it means if the point (X, y) lies: 0 inside the shadedregion? we. W M‘ML‘ MON/441, *0 Elk-l1 “Alfie: Maww'l‘s with saw. Moij leC-l W. o onaborderline? (DQ— lA-M ngac-l‘k/ Wk “Amt l?) LOU} “$51.. amounts milk no mew \epr m. 0 outside the shadedregion? LUG— do h‘i’ km, Wk NW ‘1, by“? 4M5; amounts». ...
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