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# INTRO MATH MODELING MATH 1101

UGA

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This 44 page Class Notes was uploaded by Joanne Bergnaum on Saturday September 12, 2015. The Class Notes belongs to MATH 1101 at University of Georgia taught by Reichle in Fall. Since its upload, it has received 134 views. For similar materials see /class/202078/math-1101-university-of-georgia in Mathematics (M) at University of Georgia.

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Date Created: 09/12/15

MATH FINAL A place to ask questions work problems together exchange last wills and testaments consolidate notes and contemplate the reality of an uncaring universe after that ladder problem Helpful Stuff at the top go to insert gt equation mathwaycom kooferscom has backtests you can sign into chat to chat good forworking through problems Problems on the Final There are 20 questions with 50 answers he explicitly said there won t be a question about distance from home on the final exam while we were learning it the rest of what s in my notes overlaps with testsquizzes 1 13 One of 18 20 Probably about 2 answers a hx x 3 b hx x2 7 c hx m 2 14 One like 58 finding ARC Probably about 4 answers 3 Questions from the study sheet he gave out on Friday Probably 10 answers a Could someone add some of those questions to this doc Maybe we can work them out together H added below 4 Evaluate determinants Probably about 1 answer 5 Best Fit Probably about 7 answers a only regression problem b best fit linear equation average error c best fit quadratic d best fit exponential e which is the best fit Cheat Sheet Worksheet Determine whetherthe following describe functions that are linear or exponential For parts ac write the formula for the amount of money At in the account in t years t years since 112000 For parts d and e write the formula for the population Pt in thousands of a city in t years t years since 111995 AC reset to zero DE reset to 1995 a You invest 500 on 112000 and the value decreases 6 each year c Exponential o It changes by the same percent each year 0 Variable will be an exponent 0 We don t divide the interest rate by 12 it s not compounded monthly it s yearly Formula we use is At A0 1 rquott rlt 0 What s in parenthesis can never be negative even though it s decreasing and it s not 1r because it s decreasing So the function is 500 106 t b You invest 500 on 1I1l2000 and the value doubles every 8 years c Exponential o Increasesdecreases by the same percent or factor every year so t will be exponential 0 It s not raised to 2t wrong because that s twice a year We re not compounding semiannually 0 So the formula we use is At Aobquottn which is a 33 problem 0 So the function is 500 2 Atl8 is it supposed to be multiplied or divided lt I might have written it down wrong so i have no idea Divided since it is happening every 8 years c You invest 500 on 1I1l2000 and the value increases 50 every 2 years 0 Linear o Increases by the same amount not the same percentfactor 0 Variable is not an exponent so formula we use must be something like mxb I m average rate of change I b output when input is zero reset value I 0 output is 500 0 ARC average rate of change when input increases by 1 output changes by the ARC 0 When the year increases by one the amount increases by 25 502 25 a year 0 So the function is 500 50tlZ or 500 25t d On 1I11995 the population of the city is 50 thousand and on 1I1l2000 the population is 60 thousand and the population grew naturally by the same amount each year between 1995 and 2000 0 Linear 0 Increase by the same amount each year 0 Check your answerwith these Plug it in o mxb b is output when input is 0 starting amount 0 b 50 0 ARC m 6050 lt input ARC 2 50 lt output 0 So function is Pt 502t e On 111995 the population of the city is 50 thousand and on 112000 the population ofthe city is 60 thousand and the population grew naturally at the same percentage rate each year between 1995 and 2000 o Exponential 0 Function is e 506050quotT5 Review Material Evaluate Determinants 8 6 3 2 7 9 1 8 6 0 Make matrix 3x3 0 2nd quit 0 2nd matrix math 1 det enter 0 2nd matrix 1 A enter close parenthesis 0 so detA 231 Best Fit 1 m1 0 132 10 187 20 254 30 346 40 466 find 0 best fit linear formula and average 0 best fit quadratic formula and average 0 best fit exponential formula and average 0 which is best Put in table stat a 1 edit a enter a L1 t L2 pt Go to stat a calc a o LinReg 4 o QuadReg 5 o Epreg 0 Just press enter because no need to put in Y1 This gives you the formula In your calculator you re going to enter lsumResid2n o n of things undert here it s 5 o to get resid 2nd a list a 7 Resid 0 sum 2nd a list a math a 5 sum c To get this formula again simply use 2nd entry Formula Average Error best fit linear 827x1116 18 674 best fit quadratic 111x2 2841x133743 2325 lt smallest best fit exponential 134391 X1032 3258 Best Fit 0 formula that gives you the lowest average error 0 So here quadratic is the best fit Formulas amp Other Info Formulas how to work problems and calculator methods Oh my Unit1 f x f of x output input oulpi jcieperident inputindependent Functions y x2 y x Not Functions xy2 X M Functions 0 F00 is not a function if there is more than one output sharing the same input 0 F00 can be a function if there are multiple or several inputs for the same output ARC change in y y2 y change in x X2 x1 x is when decreasingincreasingconstant one like 58 in the book in section 14 7 ARC 6 92 3 32 function is going down from left to right 18 6 etc fx is decreasing at an increasing rate because ARC is increasing when ARC is decreasing is decreasing 13 ONE OF THESE WILL BE ON THE FINAL always use or for infinity 18 x3 D R1 191273 D 32 co R 0 co 20 x2 7 D eo co R 7 co 0 including 0 o up to and not including infinity For domain do we set the problem equal to zero and for range plug in zero Trying to figure how you got 7 forthe range on the last one ehh does that help Yup thanks no problem 0 Graph it o 19 32 0 o 20 0 7 hx xquot2 7 Hquot R lowest amp highest value can be c R 7 as e 7 smallest x not the smallest x but smallest y X can be a negative number that s why the domain is infinity to infinity The smallest y can be though is 7 can be is 0 smallest 0quot27 can be is 7 0 what can you square and add 7 to all s o xquot2 is always greater than or equal to 0 Forwards 39 12 375 t quot What is this one for e i don t actually remember i think it was resetting the clock when we first learned it we probably won t need to know this quotyear quot october 0 april 25 0 july 50 o october 75 Backwards Function in y1 o Backwards value in y2 0 set xmin and ymax 0 zoom a 0 0 2nd calc intersection enter x3 0 ex 11157 0 year 11 year eg 1999 2010 o 12 X decimal eg 157 1884 How do you know when to reset the clock and when not to My notes say most likely when dealing with years 23 Possible piecewise linear function Population model 13 ordered pair 1950 45 and use pointslope idk if you reset the clock sometimes he did other times he didn t the ARC will have to be given either will give you two ordered pairs or the actual ARC In this case the actual ARC was given Pt 45 109 t 1950 1950 E t 1970 if told to reset 0 lt tlt 30 and the equation is 45 109t 263 75 t 1970 t lt 1970 told to reset equation becomes 263 75 t 20 and your domain istlt 20 to get 263 choose a common point between both equations usually the last domain value of the first equation ie 1970 or 20 i like 20 easierto deal with plug in 20 fort in the first equation and solve Basically When t is 20 the y coordinate is 263 Hope that helps Unit 2 Annual Growth rate solving for Only look at the growth factor or the 1 r Year factor plug in the given year for t Example Pt 163 7632 l tl7 Annual growth rate 7632quot 171 0378 x 100 378 7 year factor 7632 1 2368 l u ml 3 mile Mills 2quot ou plug in 7fortbecause that is the year growth factor 77 1 So basically you can ignore that part because anything raised to the 1 power is itself Then you take what s within the s and subtract 1 Next multiply by 100 This was kind of easy i can put one up where its 1068 or something like that if you want The 7632 the annual growth factor you are trying to nd the rate or solve for r If that clears it up 1 r 7632 These are ones I did with him outside class so I am pretty sure they are right The annual growth rate popped up on the quiz and test 31 o At Ao1rt rgt 0 lt increasing 32 o AtA0 1 r rlt 0 lt things decliningdecaying to find intercept with two put one in y1 one in y2 tblset zoomfit calc intersect graph a A4 AavVo u atervame Engm mumes mam rurAu m became Wu oflncrease quot An Agony Ease Rate Am Aob W Population at Two Dmeremnmes A0 vAo msaxwa ysw A CD 1n sumeune gm wermaw Suny me banana prnb1emltr Number 251nm bunk a 131 1 49 29449quotL 1115 15 an annuahsu there 15 nu my 15 r 1 45 1 huur ASEEI 75 mmules Y1 1 75 1127 bacteria Y L Bhuurs 2pm 3 15pm WED duck and assmmutes x e 21 mmutes s The many formula s of chapter 3 If given an initial value and a new value use this formula A0 vAo if given an multiplier doubling tripling etc use this formula A0 Aob If given a rate whether increasingdecreasing use either one ofthese formula s At A01rtquot 0 they all equal the same thing and will give you the same answer Some are just easier to do given certain criteria trr Unit 3 DOES ANYONE KNOW HOW TO DO THE MUMMY PROBLEM ON TEST 3 IT S 3 HELP lt see bottom 41 o compounding n times per year AtAo1rn 0 continuous compounding At Pert o to find effective annual yield or rate 0 invest100 for1 year subtract100 0 continuous growthdecay A0 Aoe we 5152 0 fx 2x2 bxc lt standard form 0 if a gt 0 parabola opens up 0 if a lt 0 parabola opens down 0 c is yintercept 0 fx axhkk lt vertex form 0 same a as above 0 hk is vertex 0 fx ax2bxc0 o 2 solutions if b274a gt 0 o 1 solutions if b274a 0 o 0 solutions if b274a lt 0 o projectile motion ht 71622vo d height in feet time in decimal o vo initial velocity in feetseconds I 0 if object is dropped I gt0 if object is thrownfired upward I lt0 if object is thrownfired downward Population Model 0 to reach a given level put in y2 and intersect 0 initial population a 0 will double put in y2 intersect convert to date year and month 0 predicted population at x date date initial date y1that Distance 0 how long stays in air a calculate zero 0 left xmin right xmax how deep is well 0 set up function 0 no height or velocity 0 y13 answer how long takes to hit bottom given depth 0 depth716x200 max amp min a set cursor max a put in y1 L1 input data L2 output data L3 Y1L1 L4 L2 L3 L5 L42 sumL5 SSE Vansn average error Unit4 61 Finding SolutionsZeros o Enterfunction into Y1 Y 0 Check the graph to see approximately where the zeros are 0 SOLVE a Solve Y1 X I 2 CATALOG I scroll to solve ENTER 0 VARS a YVARS a function a Y1 a ENTER 0 COMMA above 7 on calculator o ALPHA ax COMMA above 7 on calculator closest to where the solution is close parenthesis above 9 on calculator Volume 0 Function for the volume only Vx a x b x c x 0 Finding Vx in equation above a X b X 0 times 1 greater than asa decimal o Enterthe following function into Y1 Y a x b x c x 7 Vx c Find zeroes I See FINDING SOLUTIONSZEROS or I 2 CALC a zero a enter left and right bound eg left bound 5 enter 0 This gives you xegx433 0 Volumes are a x b x and cx Square Cut Out 0 vxltp2xgtltq72xgt c There are two solutions for x e Fwd zems Ladder quotJ 3 lusidmi h Perfect a hnha a th haw We ve aHjus accemed dEVEa WNh the mang e pyemem t Gum 24 Wkava s u gum W because 24 s puve gum basmaHym a u mmuve x y gvams mm HWZAy gvamstQA Cums New Mmuve Detevmmams yeah de evmmam m m an n USE MATWX g1 basically bottom all the things you d put in matrix one top x last row 2nd 2nd to last top y 1st row last 2nd to last Quiz 1 1 Is it a function a Does the equation y x2 represent y as a function of x b Does the equation x y2 represent y as a function of x 2 Finding domain and range a State the domain and range of the function yx27 b In June 2005 Tmobile advertised a Get More Pan for cell phone service that included 600 whenever minutes each month for 4000 with additional minutes charged at 40 cents each This plan describes a function Cn monthly cost G as a function of additional minutes n Using the appropriate set notation state the domain and range of this function 3 Given the function below fill in the last row ofthe table by computing the average rate of change AyAx for each successive pair of points and then complete the sentence below the table by choosing the correct word in both parenthesis x 1 0 4 11 23 fx 12 9 3 6 18 AyAx The function is 39 39 39 39 at an I39 39 39 39 1 rate 4 Given the following information find a linear population function Pt where t year and P the population P1990 725 and P2002 605 The number of calories that a person burns depends not only on what type of activity is performed but also on the person s weight A person who weighs 130 pounds will burn 590 calories playing racquetball competitive for an hour while a 155pound person will burn 704 calories doing the same activity Find a linearfunction Cw that gives the number of calories burned per hour of competitive racquetball as a function of weight Assume that the population of city A is given by Pt25028t and the population of City B is given by Pt200 33t where P the population in thousands and t years since 1990 a Find the month and year in which both cities have the same population 01 0 b What is that common population Write your answer in thousands accurately to two decimals Test 1 MthO TEST A Name K v 1 Decide whethery is a function ofx Answer ye or m a 1116 mnow mg table x I2 4 4 5 s w y 2 4 A 5 3 w b The followmg funnl a x M 2 v H W39 5 following a 39 Domain Rangtl Decreasing ovcz the intervals and Increasing over the mterval 3 cmer A L ether J 71 1 2 1 5 1 11 x 18 113 s H 44 AyAx Overl0 Over012 Over1251 Over1s101 The function is mm rate Th 1m 1 39 ui alhmm 39 39 11 124942 when C 20 and L 125131 when c 1111 nd a linear function my mm gives the lenglh 0139 the red as a runcuou of 11s Celsius lemperatuxe r A m 1 1 MO 39J 39 I I 39 quot l I I I9 5 39 39 39 accolding 1a 1112 funnula P0 355 171 where m is the population in thousands and 1 years since 111935 mi resels the clock Chy B has a pnpulalion 1145325 1housaml on 111983 and is 39 I 1 1 1197A Iv i l11391985 Find lhe munlh mu mcnum 11 I I I I I I I 5111551 populmions are equam Year Month Populauon 6 The populalion oFCiiy Kwas 375 111mm 111 1900 and from 1900 10 1950 it declined at the average me on 1 m From 39 V c A V 39 I I rr 39PUH 393 I1 1 I PU 7 sllt 7 39l39heConsunH 39 mequot n consumers For housing for selected years 1987 m 1996 Pm b Using your saved model Mm should be the cm in 19917 CPI 39 J I nu am y a I9501hroughl99035 Pl1856r4472where I Find the SSE and the average error for this modal m 0 mamams 674 SSE Average Error Quiz 2 does anyone remember how to set up the rabbit problem 312425 o 6156quotans Test 2 Give all decimal answers will al leasl lwn decimals 1 b l l 1 y l 10 l 20 l 40 Y I 0 l l I z 10 l 20 l 40 Linear funmion Exponemiol function y 2 Wills malllemalical models 0139th form P0 pD 47 a years dial sausfy m following conditions a He 32 and Pdecrcascs 47 every 9 ycaxs Pl V b ml 135 and P quadruplesevery 25 years Pm c A naturally growing population of a cily was 43 ll39musimd in 1930 and 37 mousmrl in 2000 101 1701 mo population in thousands years aim 1980 P0 g 3 TheFi ingll A 39 AmPl39lr Qh 02 PH quotquot A quot L 39 39 N764 and 95 52 billion dollars in 1994 a 39 h 39 charitable giving ovsrlliis in period Annual percent increase two decllmls b u 39 39 Americans in 2004 4 A naturally growing bacteria populmion m numbers 33 at moo am a P0 or How many booieria are here all 115 pm Quiz 3 Test 3 1 What is me annual m vs 723 with inlcmst Compound a Qumany b Continuously decimal places a 723 compounded quancny b 728 compounded cominuously n m I vil 39 39 39 A v 14 remains How old i lh mumm carbonl4 s U Ull yn Agc ofmummy years 39 39 bx L is posiuvc negative or zero Circle your answer a a positive negative zero b a positive negative zero c bim positive negative zero has no maximum or minimum value write Noue a x 3x 37 forx in Lhe domain of f Maximum h x 73x 1 3 forx in me imerval i SK 3 Maxu39nunl C x 3 3x3ifm xinthcimervul45x58 imum 39 iflh function Minimum Minimum Minimum building 103 feet high a when does Ihe ball reach is maximum height h Ilaw long docs the bull remain in the air 9 Whai is ihc maximum height 11 when does Ihc Dali reach the lap of ihe building on me way down 6 Whal is Ihe height nl39lhe bail a er 575 second7 wall a 15 feet per second Him lung did i lake the smne to hi the walel n the U xvcar i 1930 i i940 1950 1950 i 1930 i 1990 Pm I 116 83 59 s4 51 i 79 i a L J pmbandcRoundln3dechnal places Pr 17 Find an any cmrofyoux saved optimal qundmlic modal I0 n 39 muucn c Quiz 4 if you can t read 1 it s 1008xquot4 1914x 36443XA25104x10200 Test 4 Find all solutions to me equau39on sv x 120J 6650x 2375 6750 0 Write your answers as inkgels or simglg actions only A2inchby4idbquot L quot 39 quot 39 J hu dbl n 1 n L L u f the unplaled block a Give the mm39on for the volume only of the plmed block W In What am Lhc dimcnsions of the planted block an nu puregoldand L AZ karal gold Letx be the grams of J on lSkmt gold N 1 Zkamt gold a Shaw lhv two cqualions necessary to solve this problem 11 um um w WWW mm grams of pure gold gnun5 of l4 kml gold Solve the following system of equatinns It is not necessary to shawyour work 3w2x7y52 492 2w 4x 39Gz 424 5wx7y 3z276 W quot 4w 6x 8y9z 446 3 39 39 39 39 NF Tl V show your work No credit 39quotL 39 39 39 tr ma 4 second variable 5x5y 3 7r8y75 39 Yau mus show me expansion 0 gal credir for we answer 5 777 4 o 2 u 4 99 5 7 r L X 8 A l 39 gt How Far i 1 Fa mr a muul Mgold problem was offlry 3 You wan 72 grams nl l4karal 39 39 gmle b l l I 39 4 72 grams of Mkam gold a Show me two equations necessary to solve this problem b Find u ml 1 39 39 39 w H shu grams of pure gold grams 0mm gold QampA For questions hlln39lwww 39 h l I 39 rleIarlrler hlm Fquot This may ease some ladder problem woes quot 39 a problem quot39 MATH FINAL A place to ask questions work problems together exchange last wills and testaments consolidate notes and contemplate the reality of an uncaring universe after that ladder problem Helpful Stuff at the top go to insert gt equation mathwaycom kooferscom has backtests you can sign into chat to chat good forworking through problems Problems on the Final There are 20 questions with 50 answers he explicitly said there won t be a question about distance from home on the final exam while we were learning it the rest of what s in my notes overlaps with testsquizzes 1 13 One of 18 20 Probably about 2 answers a hx x 3 b hx x2 7 c hx m 2 14 One like 58 finding ARC Probably about 4 answers 3 Questions from the study sheet he gave out on Friday Probably 10 answers a Could someone add some of those questions to this doc Maybe we can work them out together H added below 4 Evaluate determinants Probably about 1 answer 5 Best Fit Probably about 7 answers a only regression problem b best fit linear equation average error c best fit quadratic d best fit exponential e which is the best fit Cheat Sheet Worksheet Determine whetherthe following describe functions that are linear or exponential For parts ac write the formula for the amount of money At in the account in t years t years since 112000 For parts d and e write the formula for the population Pt in thousands of a city in t years t years since 111995 AC reset to zero DE reset to 1995 a You invest 500 on 112000 and the value decreases 6 each year c Exponential o It changes by the same percent each year 0 Variable will be an exponent 0 We don t divide the interest rate by 12 it s not compounded monthly it s yearly Formula we use is At A0 1 rquott rlt 0 What s in parenthesis can never be negative even though it s decreasing and it s not 1r because it s decreasing So the function is 500 106 t b You invest 500 on 1I1l2000 and the value doubles every 8 years c Exponential o Increasesdecreases by the same percent or factor every year so t will be exponential 0 It s not raised to 2t wrong because that s twice a year We re not compounding semiannually 0 So the formula we use is At Aobquottn which is a 33 problem 0 So the function is 500 2 Atl8 is it supposed to be multiplied or divided lt I might have written it down wrong so i have no idea Divided since it is happening every 8 years c You invest 500 on 1I1l2000 and the value increases 50 every 2 years 0 Linear o Increases by the same amount not the same percentfactor 0 Variable is not an exponent so formula we use must be something like mxb I m average rate of change I b output when input is zero reset value I 0 output is 500 0 ARC average rate of change when input increases by 1 output changes by the ARC 0 When the year increases by one the amount increases by 25 502 25 a year 0 So the function is 500 50tlZ or 500 25t d On 1I11995 the population of the city is 50 thousand and on 1I1l2000 the population is 60 thousand and the population grew naturally by the same amount each year between 1995 and 2000 0 Linear 0 Increase by the same amount each year 0 Check your answerwith these Plug it in o mxb b is output when input is 0 starting amount 0 b 50 0 ARC m 6050 lt input ARC 2 50 lt output 0 So function is Pt 502t e On 111995 the population of the city is 50 thousand and on 112000 the population ofthe city is 60 thousand and the population grew naturally at the same percentage rate each year between 1995 and 2000 o Exponential 0 Function is e 506050quotT5 Review Material Evaluate Determinants 8 6 3 2 7 9 1 8 6 0 Make matrix 3x3 0 2nd quit 0 2nd matrix math 1 det enter 0 2nd matrix 1 A enter close parenthesis 0 so detA 231 Best Fit 1 m1 0 132 10 187 20 254 30 346 40 466 find 0 best fit linear formula and average 0 best fit quadratic formula and average 0 best fit exponential formula and average 0 which is best Put in table stat a 1 edit a enter a L1 t L2 pt Go to stat a calc a o LinReg 4 o QuadReg 5 o Epreg 0 Just press enter because no need to put in Y1 This gives you the formula In your calculator you re going to enter lsumResid2n o n of things undert here it s 5 o to get resid 2nd a list a 7 Resid 0 sum 2nd a list a math a 5 sum c To get this formula again simply use 2nd entry Formula Average Error best fit linear 827x1116 18 674 best fit quadratic 111x2 2841x133743 2325 lt smallest best fit exponential 134391 X1032 3258 Best Fit 0 formula that gives you the lowest average error 0 So here quadratic is the best fit Formulas amp Other Info Formulas how to work problems and calculator methods Oh my Unit1 f x f of x output input oulpi jcieperident inputindependent Functions y x2 y x Not Functions xy2 X M Functions 0 F00 is not a function if there is more than one output sharing the same input 0 F00 can be a function if there are multiple or several inputs for the same output ARC change in y y2 y change in x X2 x1 x is when decreasingincreasingconstant one like 58 in the book in section 14 7 ARC 6 92 3 32 function is going down from left to right 18 6 etc fx is decreasing at an increasing rate because ARC is increasing when ARC is decreasing is decreasing 13 ONE OF THESE WILL BE ON THE FINAL always use or for infinity 18 x3 D R1 191273 D 32 co R 0 co 20 x2 7 D eo co R 7 co 0 including 0 o up to and not including infinity For domain do we set the problem equal to zero and for range plug in zero Trying to figure how you got 7 forthe range on the last one ehh does that help Yup thanks no problem 0 Graph it o 19 32 0 o 20 0 7 hx xquot2 7 Hquot R lowest amp highest value can be c R 7 as e 7 smallest x not the smallest x but smallest y X can be a negative number that s why the domain is infinity to infinity The smallest y can be though is 7 can be is 0 smallest 0quot27 can be is 7 0 what can you square and add 7 to all s o xquot2 is always greater than or equal to 0 Forwards 39 12 375 t quot What is this one for e i don t actually remember i think it was resetting the clock when we first learned it we probably won t need to know this quotyear quot october 0 april 25 0 july 50 o october 75 Backwards Function in y1 o Backwards value in y2 0 set xmin and ymax 0 zoom a 0 0 2nd calc intersection enter x3 0 ex 11157 0 year 11 year eg 1999 2010 o 12 X decimal eg 157 1884 How do you know when to reset the clock and when not to My notes say most likely when dealing with years 23 Possible piecewise linear function Population model 13 ordered pair 1950 45 and use pointslope idk if you reset the clock sometimes he did other times he didn t the ARC will have to be given either will give you two ordered pairs or the actual ARC In this case the actual ARC was given Pt 45 109 t 1950 1950 E t 1970 if told to reset 0 lt tlt 30 and the equation is 45 109t 263 75 t 1970 t lt 1970 told to reset equation becomes 263 75 t 20 and your domain istlt 20 to get 263 choose a common point between both equations usually the last domain value of the first equation ie 1970 or 20 i like 20 easierto deal with plug in 20 fort in the first equation and solve Basically When t is 20 the y coordinate is 263 Hope that helps Unit 2 Annual Growth rate solving for Only look at the growth factor or the 1 r Year factor plug in the given year for t Example Pt 163 7632 l tl7 Annual growth rate 7632quot 171 0378 x 100 378 7 year factor 7632 1 2368 l u ml 3 mile Mills 2quot ou plug in 7fortbecause that is the year growth factor 77 1 So basically you can ignore that part because anything raised to the 1 power is itself Then you take what s within the s and subtract 1 Next multiply by 100 This was kind of easy i can put one up where its 1068 or something like that if you want The 7632 the annual growth factor you are trying to nd the rate or solve for r If that clears it up 1 r 7632 These are ones I did with him outside class so I am pretty sure they are right The annual growth rate popped up on the quiz and test 31 o At Ao1rt rgt 0 lt increasing 32 o AtA0 1 r rlt 0 lt things decliningdecaying to find intercept with two put one in y1 one in y2 tblset zoomfit calc intersect graph a A4 AavVo u atervame Engm mumes mam rurAu m became Wu oflncrease quot An Agony Ease Rate Am Aob W Population at Two Dmeremnmes A0 vAo msaxwa ysw A CD 1n sumeune gm wermaw Suny me banana prnb1emltr Number 251nm bunk a 131 1 49 29449quotL 1115 15 an annuahsu there 15 nu my 15 r 1 45 1 huur ASEEI 75 mmules Y1 1 75 1127 bacteria Y L Bhuurs 2pm 3 15pm WED duck and assmmutes x e 21 mmutes s The many formula s of chapter 3 If given an initial value and a new value use this formula A0 vAo if given an multiplier doubling tripling etc use this formula A0 Aob If given a rate whether increasingdecreasing use either one ofthese formula s At A01rtquot 0 they all equal the same thing and will give you the same answer Some are just easier to do given certain criteria trr Unit 3 DOES ANYONE KNOW HOW TO DO THE MUMMY PROBLEM ON TEST 3 IT S 3 HELP lt see bottom 41 o compounding n times per year AtAo1rn 0 continuous compounding At Pert o to find effective annual yield or rate 0 invest100 for1 year subtract100 0 continuous growthdecay A0 Aoe we 5152 0 fx 2x2 bxc lt standard form 0 if a gt 0 parabola opens up 0 if a lt 0 parabola opens down 0 c is yintercept 0 fx axhkk lt vertex form 0 same a as above 0 hk is vertex 0 fx ax2bxc0 o 2 solutions if b274a gt 0 o 1 solutions if b274a 0 o 0 solutions if b274a lt 0 o projectile motion ht 71622vo d height in feet time in decimal o vo initial velocity in feetseconds I 0 if object is dropped I gt0 if object is thrownfired upward I lt0 if object is thrownfired downward Population Model 0 to reach a given level put in y2 and intersect 0 initial population a 0 will double put in y2 intersect convert to date year and month 0 predicted population at x date date initial date y1that Distance 0 how long stays in air a calculate zero 0 left xmin right xmax how deep is well 0 set up function 0 no height or velocity 0 y13 answer how long takes to hit bottom given depth 0 depth716x200 max amp min a set cursor max a put in y1 L1 input data L2 output data L3 Y1L1 L4 L2 L3 L5 L42 sumL5 SSE Vansn average error Unit4 61 Finding SolutionsZeros o Enterfunction into Y1 Y 0 Check the graph to see approximately where the zeros are 0 SOLVE a Solve Y1 X I 2 CATALOG I scroll to solve ENTER 0 VARS a YVARS a function a Y1 a ENTER 0 COMMA above 7 on calculator o ALPHA ax COMMA above 7 on calculator closest to where the solution is close parenthesis above 9 on calculator Volume 0 Function for the volume only Vx a x b x c x 0 Finding Vx in equation above a X b X 0 times 1 greater than asa decimal o Enterthe following function into Y1 Y a x b x c x 7 Vx c Find zeroes I See FINDING SOLUTIONSZEROS or I 2 CALC a zero a enter left and right bound eg left bound 5 enter 0 This gives you xegx433 0 Volumes are a x b x and cx Square Cut Out 0 vxltp2xgtltq72xgt c There are two solutions for x e Fwd zems Ladder quotJ 3 lusidmi h Perfect a hnha a th haw We ve aHjus accemed dEVEa WNh the mang e pyemem t Gum 24 Wkava s u gum W because 24 s puve gum basmaHym a u mmuve x y gvams mm HWZAy gvamstQA Cums New Mmuve Detevmmams yeah de evmmam m m an n USE MATWX g1 basically bottom all the things you d put in matrix one top x last row 2nd 2nd to last top y 1st row last 2nd to last Quiz 1 1 Is it a function a Does the equation y x2 represent y as a function of x b Does the equation x y2 represent y as a function of x 2 Finding domain and range a State the domain and range of the function yx27 b In June 2005 Tmobile advertised a Get More Pan for cell phone service that included 600 whenever minutes each month for 4000 with additional minutes charged at 40 cents each This plan describes a function Cn monthly cost G as a function of additional minutes n Using the appropriate set notation state the domain and range of this function 3 Given the function below fill in the last row ofthe table by computing the average rate of change AyAx for each successive pair of points and then complete the sentence below the table by choosing the correct word in both parenthesis x 1 0 4 11 23 fx 12 9 3 6 18 AyAx The function is 39 39 39 39 at an I39 39 39 39 1 rate 4 Given the following information find a linear population function Pt where t year and P the population P1990 725 and P2002 605 The number of calories that a person burns depends not only on what type of activity is performed but also on the person s weight A person who weighs 130 pounds will burn 590 calories playing racquetball competitive for an hour while a 155pound person will burn 704 calories doing the same activity Find a linearfunction Cw that gives the number of calories burned per hour of competitive racquetball as a function of weight Assume that the population of city A is given by Pt25028t and the population of City B is given by Pt200 33t where P the population in thousands and t years since 1990 a Find the month and year in which both cities have the same population 01 0 b What is that common population Write your answer in thousands accurately to two decimals Test 1 MthO TEST A Name K v 1 Decide whethery is a function ofx Answer ye or m a 1116 mnow mg table x I2 4 4 5 s w y 2 4 A 5 3 w b The followmg funnl a x M 2 v H W39 5 following a 39 Domain Rangtl Decreasing ovcz the intervals and Increasing over the mterval 3 cmer A L ether J 71 1 2 1 5 1 11 x 18 113 s H 44 AyAx Overl0 Over012 Over1251 Over1s101 The function is mm rate Th 1m 1 39 ui alhmm 39 39 11 124942 when C 20 and L 125131 when c 1111 nd a linear function my mm gives the lenglh 0139 the red as a runcuou of 11s Celsius lemperatuxe r A m 1 1 MO 39J 39 I I 39 quot l I I I9 5 39 39 39 accolding 1a 1112 funnula P0 355 171 where m is the population in thousands and 1 years since 111935 mi resels the clock Chy B has a pnpulalion 1145325 1housaml on 111983 and is 39 I 1 1 1197A Iv i l11391985 Find lhe munlh mu mcnum 11 I I I I I I I 5111551 populmions are equam Year Month Populauon 6 The populalion oFCiiy Kwas 375 111mm 111 1900 and from 1900 10 1950 it declined at the average me on 1 m From 39 V c A V 39 I I rr 39PUH 393 I1 1 I PU 7 sllt 7 39l39heConsunH 39 mequot n consumers For housing for selected years 1987 m 1996 Pm b Using your saved model Mm should be the cm in 19917 CPI 39 J I nu am y a I9501hroughl99035 Pl1856r4472where I Find the SSE and the average error for this modal m 0 mamams 674 SSE Average Error Quiz 2 does anyone remember how to set up the rabbit problem 312425 o 6156quotans Test 2 Give all decimal answers will al leasl lwn decimals 1 b l l 1 y l 10 l 20 l 40 Y I 0 l l I z 10 l 20 l 40 Linear funmion Exponemiol function y 2 Wills malllemalical models 0139th form P0 pD 47 a years dial sausfy m following conditions a He 32 and Pdecrcascs 47 every 9 ycaxs Pl V b ml 135 and P quadruplesevery 25 years Pm c A naturally growing population of a cily was 43 ll39musimd in 1930 and 37 mousmrl in 2000 101 1701 mo population in thousands years aim 1980 P0 g 3 TheFi ingll A 39 AmPl39lr Qh 02 PH quotquot A quot L 39 39 N764 and 95 52 billion dollars in 1994 a 39 h 39 charitable giving ovsrlliis in period Annual percent increase two decllmls b u 39 39 Americans in 2004 4 A naturally growing bacteria populmion m numbers 33 at moo am a P0 or How many booieria are here all 115 pm Quiz 3 Test 3 1 What is me annual m vs 723 with inlcmst Compound a Qumany b Continuously decimal places a 723 compounded quancny b 728 compounded cominuously n m I vil 39 39 39 A v 14 remains How old i lh mumm carbonl4 s U Ull yn Agc ofmummy years 39 39 bx L is posiuvc negative or zero Circle your answer a a positive negative zero b a positive negative zero c bim positive negative zero has no maximum or minimum value write Noue a x 3x 37 forx in Lhe domain of f Maximum h x 73x 1 3 forx in me imerval i SK 3 Maxu39nunl C x 3 3x3ifm xinthcimervul45x58 imum 39 iflh function Minimum Minimum Minimum building 103 feet high a when does Ihe ball reach is maximum height h Ilaw long docs the bull remain in the air 9 Whai is ihc maximum height 11 when does Ihc Dali reach the lap of ihe building on me way down 6 Whal is Ihe height nl39lhe bail a er 575 second7 wall a 15 feet per second Him lung did i lake the smne to hi the walel n the U xvcar i 1930 i i940 1950 1950 i 1930 i 1990 Pm I 116 83 59 s4 51 i 79 i a L J pmbandcRoundln3dechnal places Pr 17 Find an any cmrofyoux saved optimal qundmlic modal I0 n 39 muucn c Quiz 4 if you can t read 1 it s 1008xquot4 1914x 36443XA25104x10200 Test 4 Find all solutions to me equau39on sv x 120J 6650x 2375 6750 0 Write your answers as inkgels or simglg actions only A2inchby4idbquot L quot 39 quot 39 J hu dbl n 1 n L L u f the unplaled block a Give the mm39on for the volume only of the plmed block W In What am Lhc dimcnsions of the planted block an nu puregoldand L AZ karal gold Letx be the grams of J on lSkmt gold N 1 Zkamt gold a Shaw lhv two cqualions necessary to solve this problem 11 um um w WWW mm grams of pure gold gnun5 of l4 kml gold Solve the following system of equatinns It is not necessary to shawyour work 3w2x7y52 492 2w 4x 39Gz 424 5wx7y 3z276 W quot 4w 6x 8y9z 446 3 39 39 39 39 NF Tl V show your work No credit 39quotL 39 39 39 tr ma 4 second variable 5x5y 3 7r8y75 39 Yau mus show me expansion 0 gal credir for we answer 5 777 4 o 2 u 4 99 5 7 r L X 8 A l 39 gt How Far i 1 Fa mr a muul Mgold problem was offlry 3 You wan 72 grams nl l4karal 39 39 gmle b l l I 39 4 72 grams of Mkam gold a Show me two equations necessary to solve this problem b Find u ml 1 39 39 39 w H shu grams of pure gold grams 0mm gold QampA For questions hlln39lwww 39 h l I 39 rleIarlrler hlm Fquot This may ease some ladder problem woes quot 39 a problem quot39

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