1105_LW5B_solutions_F11

# 1105_LW5B_solutions_F11 - 2 each part below y is an...

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Unformatted text preview: ' ' 2.. each part below, y_ is an exponentiai ﬁmcﬁqn ofx. You must mite the formuia. . I I I a) in a laboxatmy setting, a population of ﬂies starts at 260 ﬂies and triples every W961; :Wﬁte 2m exponentiai fuﬂctionformula that gives 52,1113 pop‘giation 3: weeks from'now. - AgsWer:;y_=.z§° (3} b) Quantity-y starts at milligrams and i5 halved each day. ;. Wztitean exponergﬁal {311191ng __ formuia that gives {he y—quantiiy 3 days from ndw. ' .. .- : . - . . '1 ' . . X -_ Answer: 3/: Zaopéj c) -. Quantity starts at 2.139111131331115 grows by a factor of 11165 _ _ 'Write'an exponentiai funcﬁdnﬁomula ﬁhat gives the y-quantity _x___h_ours_ now,_ ‘ -. d) :Quaﬁtity y starts.at100‘mﬂﬁgrétms decays by a' faciw of £1,558 every hoﬁr,‘ ' ' . 'Write apexponemiai funggion formula that givesi'the y—qﬁailtityixihoms from HOW. . - ' - - _ g 7. “a _. -- Answer: 32: Z“§_{D’5\$322; . 3. For each exponential function formula below, détcrming whether thé: fuﬁiéfiién raﬁréséms; éﬁponential growth or decaﬁthe initialqilanﬁty, the growth. or :1er factor, and the grow}: or decay rate. Sketch its graph, labeling the "vertical intercept. Your sketch should ahow the asymptotic behavior bf ' the graph} and two other points, 9113 with positive ipput and the otherﬂith nggaﬁve input. _. -= 2 _ '- ' '- _ E 73:) Q(z)=(1.2x10‘?)(1.17)' L b) P(¥}_;30(0.85)‘ ' - ' '6.) Twp-25(4)"; _ resemLPp-ﬁ - I I - - .Jecé. ' g; I “<3 m . q‘hﬂfaj rajue, “rt. I:ZK{0%'-'~ r - '3‘“; ijéwa'22305 '- I I )I'ﬂ I ' - f“ magma, 1 ' é; {Fm‘zévﬁmegfj a; P «L I I raggawﬁwswigv, -5!” ' ' 3 .. - 4. The four-graphs shown correspond to the four function foxmuiasbelow, Mags}: each graph with its fogmuie by ﬁlacing..the lefterpf the graphite the next to its formula. ‘94 / 'grnwﬁfdeee;.- W!“ . -- - _J 3. ' ; -¢- 53 32:00.1)? [teem e?» {oxalgrmﬁh _ ;_mee;e=- yecwm*.+43© e::¢%ere ‘ ' 2_ . . yéCQY; 333 +héo ..§ao‘2, 0:9 I' I 5e! ,a..._—._._._._-...._., y=c£078>x 4 an 2:3» 2,32 am: a w 5. When ﬁrst taken, 2} cold medicaﬁogl intreducee 200mg of e active dreg into the bleed _ The I. . I i r ametmt of ecﬁve drug (ieceys exponentieiiy aeeercﬁng to __the formula .50) :‘200(0.7_Q7)_’ _:;_ -' ' - a) Use the calculator’s table and graph features to estimate how long it will take for there te-be only - - . - 150 mg ofaciive drug inthe bloodstream, rounded 19 the nearest tenth of anhour day. - ' ' x:memw~-_e 55. 1935 , - - - ' - ' ._'A .%. -‘ werztss_-a_-'_ours .- Y22'15iﬁ) I ZIgCALqfinZEfSEC—i— I . _ _ . 13) Use the caieulator’s tableand graph feauues teeetimate thd half Iifefer. this. drug, rounded to the _- . We tethofehw- -* J ' " - - : . ' ' - .-.+:memm «Fee m we yi :190. (6.7197) .' '5 '.'--An_swer: f2: 2,0 . hours be {ﬂosng-gu 19075913 Yea-1G0 ' 1“";ce\c,_1n reefer .'x:;.qﬁ912.3¢1m -. . _; " .- - -. -. . - _ - . .- ) Use the realcuiator’s table and graph features to {asexuate when only{§5%roffheinitia1amounbjs - _ still a ﬁve inthe blood stream, mended to the neaxest tenth of an hem. _ 3- ' '61_§'f){;¢g3§ 2;; 3 Q .¥ #3:! .Answex:1re bib hours 7-" '- 25", caiqiniéme : Keiwetre‘: r - ' .- ' - .. - “- (1) Sketch the glaph andlabel the points 01:; the graph conesp ding to you: answers from a)-c). _ _ _. it; beef-0.37? ' Yam-ca_ns+aei°- .150! emmgfeeud 3g) 6. A muiual fund account is currently velued at \$20_0.0._ _ a) .Ifthe account damages f9 \$2200 eve; seme time period? What is the piiérceﬁt: incmage Dim. 'thistimepeﬁod? " -' '- - ' . . . . Em? ' Beale-L '. - . . . '” ' ' anewmee ‘ ; ’63-‘35 --Z - j if}: 1&0?“ e_ :10 W. I b) Ifthe aceeuntde'ceeases to \$1700 osfe‘I-ﬂﬁeﬁmeperiod,whet_'isthe15erce1}t decreaeeover. U thistimeperidd?-- " -. .. .. _. ._ _ . ._ : .moewaeaa ' MLwWMM 2x we in »_ . we) .—~ . 5 . .. lb. " . gems ;--; ;- . _: -_ %_ :5 7. The vaiue of'a condog'ninimn is currently \$100,000. ' -' . If its value Epcreascs by 10% pic: sometime periodgfmdﬂge increase in vahw'andjhe _- .3 ' condo_"s_ya1ue aﬁhe 3nd pf.t_hi.fs_time__peri0_d._ .-; ' - - - ' .- ' iogégogiff’ AIQGO‘W‘Q‘C’) {.Oféjgxgwers:§aqea§einvahie:\$ \$0 {363\$}; :11 ' __eahc\_\rcg\¢e_ 353190,??? % \ogooéﬁimﬂmQ Césido’é.valua=-.\$Ji_ci£%€3_f' ' Now We I b) In part 20,133! what factor did the céﬁdo’s' value increase? That is, ifwéﬁmitip.1y\$100,000 by _ i_ _' the number rIg lb. b.“ we get thq condqfs Ivalu'e' at the and ofithis Lime period-s __ ' ’ ; . ' . . . c) If its vaiue decréasés by 15%,dersome tinié period, ﬁnd #13 dBCIéaSBIiI-l valus and the _ . -' 'condo’s vakue at the and ofthis time periqd. - ' - ~ -: - . . . 15 c? :39 5-100 000 is 4‘; £09 000) i , . _ . I .c: 1 _ f _. - . Answers;I‘Decmasein-Value:\$ 1500C) Qﬂa “‘91.”?ng 55:36:00? ggggwg- _ -. " '- .' -- - = - . Mob: 2625??? - swﬁ'ﬁéﬂ 45-353 ﬁ-iwgééﬁiﬁi‘é? 7' d) In paIt‘a), by Whatﬁmmr did the condo’s Value decrease? Thai is, if we mlﬂtipiy \$100,090by ' ' the number 5 .5 w; gst tbs condok value at the and ofthis tinge pgrioti. _ ' - 3 ' ' r m___ ‘8. Thepopulation of a city grows annually by_1_._’;'%. 3' ' a) If thé population is 40,500 at some particuiaxpojjﬁ in time, ﬁndthe repulation one ygér’lat_ei._ 405‘00 {inﬁll-dadiéimenmwhgicnumyqr)I l 8 I b) In general, if wemultiply the popﬁiation at ﬁﬁynﬁbmeﬁt by the numbef s '0' 2'7? , get I ‘ '. thepopuiationone yearlatgrg '- ' ' ' -- ' " r .. ' -' -‘ c) Ifthe current popuiatidn is denotégi , mite a ﬁméﬁog formﬁla lhéﬁxépréséntsﬁbpuiati'ont .. yams into the future. Use this ﬁmcéﬁon anda graphic approach to detennizﬁle howman: ears _ Will‘ka o ulzition t9 613;}ng £9.35 hkg' F9 '3er +6 :2' ' “2 - 4»; '. ' ' " ' I _ :4._;_ . ' 3:, . . WV, .--.—.-=w- ?f. as. . - .. v‘ 1.3. 6:: (2,92?) ' x . (qu‘m c; jig: \{f I Calculeﬁnngegound Interest « "Finife Gama-011mlng . If 1? 2 original invesiment (called princépal), r : ennuai (call-ed nominal) interest rate in decimal form, 7 1'2 =_.t11_.e_ number of times each year_i_1_1ter_esti_s cqmpounded, and t: the number of years over’which interesprate is compolmded, then account value A is given by A; Pb +£J . The annual interest rate . ,' is eﬁen called the nominal rate. When'interest is compounded moreoﬁen than once each year (that is, '5 . I; > 1),__acco_unt vaiue actualiy grows faster than the nome rate suggests. faster Iate__is (failed the , Effective meme —:1]x‘10_0 gives this effective rate as epegeentage, . ' .9. An inﬁestment of \$4000 eanis 7.2%annnal (nominai) interest Round money to the nearest penny, - I . I. _ and effective interest rates t_o the neaxest thousandth of e'pereent __ - - . - - -- . . ._ : _l___d_ﬁ__ r- “Tit-1+ . I - ;;_ ' -. ' ' :- . I. ._ a) If iniexest is @mpoundtmwtﬂ the account value after 10 years andjhe eﬁ'eeﬁvexate. _ “Acesgiw50164r “View???” ' ' - Ew'gg‘feﬂx we '2. 713%7932‘186“ I I - Haifa-rm A<sé).-e 40990.93)‘L‘Qég‘ggugég -'b_) If imam is compounded daily, ﬁnd ihe account value after :0 yea-rs and the eﬂ’eCﬁveiete. - I _ ,372,\3{o§+ --'-3,;,g' =~- ' 7' , MBMWW“ 3e) i 3[HHEET.‘el1Xieee7q%¥W-?3355 I I I ' " I I ' ml -_ ' ' . . - I A02) 4 ' 3635.013”§§§@ﬁ“ ’ - , ,, r a ﬁre-~90? we??? ,ge‘ﬁﬂwlie - NaturaIEx onenﬁal Function Continuous Growthfﬁece and Continuum Com euﬁdin As n —>¥_oa , ﬁle quanﬁty [I ~> e 231828182846 5 an irratieﬁal ﬁﬁﬁlber' called Euler’s number. ' 7 I The co‘nstante is the base for the natural exponential function f e e_’_‘ . ' when. the annual (30mm) . rate is cempeeuded copﬁnuously, account valﬁeA given by I Peri},- [54:1]me ﬂm : effective rate as a percentage. 30. An invesﬂﬁent of \$4000 earns 7.2% meal (momma!) interest. Find the-aeeeuﬁt value aﬁeﬁ 10 years 3 __ . and the effective rate. Round moneytethe nearest p_enny,-and_the effeeiiye__inte1jest rate to the ' ' nearest thousmdmpf a perceet.-” '_ _ - . .' '. ._} r " ' " ' .Fnri w ';.b’?l- 1'11 ' ' ' C- - -_- ,,. mo .3: U geiwgﬁﬂ W I I H I ﬂJw’v-‘ihsk; {fjﬂkp‘ffg.1.p—rrsij:ffi . . 3:4. .-: 1.17:”: me? e 11. The amount of drug stiﬂ active inihe biood. stream thaws after the._dmg was ﬁrst administered can ' sometimes be medeled by a continuous decay model. Suppose the concentration of a ' ' pmﬁenlar drug is 2 miﬂigrams per liter of biood, and conceptration decays at aeominuous rate of 2%. . - " ' pezheur. Find a fommla ofthe fem A (2) =- Aoe“ that gives the coneeetx'atien i: house-ﬁe: it _ u . ' has been admimstexeﬁ, and use a graphic app each to estimate how-long it wili take for ' ' cezlcentraﬁoetoreach 1.5 mg/L. ' - " =_ ' - ' '3' ' II I ' ' "3 _ - '-. 15 5152's: 02" ' '_ se‘szq..wggsg . 12. The accident on April 26, 1986, at the nuclear power plant in Chemebyl, Russia, is censidezfefd .the worst nueiear disaster of the nueleazr age. Large amounts 9f the radioactive Substance CesiiuliszIS’l _ Welfe emitted into the air. ( hﬁpzifegjdkipedie.orgiwiki/Chemobyi 'di'saster ) The amount of an ' initial 1 (JO-milligmm sample of Cesium—137 remaining'aﬁerx years isgiyen by'the centijmoes.deeay . model \$10094.022951 . ' . I ._ . ' . . . la) ‘What continuous .yeaxiy decaygate does the formula suggest? - fa ‘ Z?! 5 pegyear. ' b) The half-life of a decaying substanee isihe amount oftimefer the'sﬁbstance {e :deeay by I. :5' _ 50%. Use a graphic approach to estimate the halfrlife 0f_Cesium-137,_ rounded to thenearest ;_- - year. Sketch the graph that iliustxexies your strategy. 'g woﬂzZQS'x. Half—life Is 53:15 ‘ 'r"__'yea_rs_ ' .. 50:21:30 3 ' ' " kg; If 6’ mo Wei}? 9)) e) _ natural exponential model ofthe form A (x) '; Aces-iv _.¢gm_be Iem‘itien the fame” '_ 3 I _ gm z w by letting c 2 A0 and sf; (2. Fem base a fog m) : msg#29323; made to I . four decimal pieces, anduse this reuhﬁe'd base to rewrite the nafeiel expenergﬁgl Inc-ﬁe} for ' Cesium-13? i11_'the_:fonn A(x)= Cra‘1 3._ ' " " ' ' ' ' ' ' " -_ F- x 5&02235x ' I _ .. < _ I {Iii-K maﬁa ' J ' _. ' AcessA (\$27-33? _ . - l' I _ 0 . 4;) rm“; .022”; - CQeclsLs\$3en3 thriiiwms. qnmgg‘égee 7 Ne 9:? 1*?” ‘3le” '- -- pad-p, 2,2613% 55 aiﬁmiéﬁ‘fk doom? _ ' - r gggj%§1rxg\$ emer ésgﬁgrf {gig-‘3 ...
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