Math 1314 Lab Module 3 page 4 4. For the function f(x) = 3x4 4x3 + 246x2 on rotelle brin exvianA . hit isimonvlog sill to Insbilleos pnibsal or to npla a. State the degree of the polynomial. donut (simonvlog ent efhw , de 103 anoilonul end to riquip mol belofos b. State the number of zeros the polynomial function will have. ( - x) (1 - x) (S + x) - = (x)1 .s c. Use the Rational Zero Theorem to list all of the possible rational zeros toivsned bra ByA - X = (x)m d d. Use your calculator to determine which numbers in the list of rational zeros are probable rational zeros. e. Use synthetic division to verify one rational zero. oivaried bra (mel reg estos to redmun epsieve and . sullushgA to Inemisqed :3. U ent mont elsb no bees8 0 ecpsly (smissb S of eyewear bruof) woled labor and vd betsmixoggs ed nes 0003 isits a169y f. Use synthetic division or other algebraic methods to find all remaining zeros. List all of the zeros of the polynomial function. 83608 -X6TOS POPS-XEr (X)A 800s ni must leg as jos to redmun egalevs ent elsmiles of lebom ent eau is .stos ni melee saige to redmun egs evs sil fiberq of Ishom gru eal d aril nirhiw sense exam ilvast aid aso motorut lenoils ed to oles erdt ismeini bas bail .o Joshoo bristemming isgong onleu aspnetnee stolarnos ninewenA Smeldong or to Ixsinoo enillsqaMath 1314 Lab Module 3 page 5 7. A rare species of insect was discovered in the rain forest. In order to protect the species, environmentalists declare the insect endangered and transplant the insects into a protected area. The population of the insect t months after being transplanted is given by P(t). 60(1 + 0.4t) P(t) = 0.01t+3 a. How many insects were discovered? In other words, what was the population when t = 0? b. What will the population be after 5 years? Round to the nearest whole insect. c. Determine the horizontal asymptote of P(t). Describe what the horizontal asymptote means in the context of the problem. Use the value of the horizontal asymptote in the explanation. Answer in a complete sentence using proper grammar and correct spelling. d. Sketch the graph of P(t). 7x2 -8x +11 8. State the domain, vertical asymptote and slant asymptote of the function C(x) = x - 6Math 1314 Lab Module 3 page 2 5. Analyze and sketch the polynomial functions and complete the charts below. State the degree and sign of the leading coefficient of the polynomial functions. Determine the end behavior of the graph of the functions. For 5b, write the polynomial function as a product of linear factors (in factored form). a. f(x) =-7(x + 2)3(x - 1)2(x - 3) lliw nob nat Isimonylog ent aones to jedDun ert etnie .d Zeros | Multiplicity |Crosses/Touches Degree ecnes lanois | eldizzoq |di to its tell of mate , 1 , | |+ + + 1 17 Sign End behavior b. m(x) = x3 - 4x2 Factored form: m(x) = to fail or ni atedmun noirw animeleb al jolsidalso mov 920 20195 Degree Zeros | Multiplicity Crosses/Touches Sign hes linoiler sno winev of nolaivib literdinve set s End behavior 6. Based on data from the U.S. Department of Agriculture, the average number of acres per farm x eciex ent to lis fell years after 2000 can be approximated by the model below. (Round answers to 2 decimal places.) onrem pisidspis tendto 10 noleivib quetlinva A(x) = 2078x -94458 .noBonut lsimonvlog ardi to 13x -2164 a. Use the model to estimate the average number of acres per farm in 2005. b. Use the model to predict the average number of acres per farm in 2012. c. Find and interpret the zero of the rational function. Does this result make sense within the context of the problem? Answer in complete sentences using proper grammar and correct spelling.Math 1314sq Lab Module 3 oluboM da J Nam For each of the following problems, show all work. Simplify and clearly indicate all answers. E 1. A ball is thrown vertically upward from the top of a building 160 feet tall with an initial velocity of 48 feet per second. The distance d (in feet) of the ball from the ground after t seconds is d(t) = 160 + 48t - 16t?. e pnieu (OF)? bait .s a. After how many seconds does the ball strike the ground? Write your answer in a complete sentence with proper grammar and correct spelling. d ( + ) = 0 160 + 481-162 0 -- 16 = 0(F) After 5 seconds, the + + 2 = 0 - 16 ( 10 # 3+ + to )_0 t- 5=0 ball strikes the ground - 16 ( t+ 2 ) ( t-5) = 0 Joenoo bas ismmsip req010 rhiw sonelee stol L + = - 2 ( F ) 1=15 Guonut art/ to cies s Of al d b. When will the ball reach its maximum height? What is the maximum height of the ball? Write your answers in a complete sentence with proper grammar and correct spelling. d( +)160+ 48+- 16+2 1( #) - 16+ 2+ 48+ +160 * = - b 20 * = - - 48 2(-16 = 1, 5 & tend to |0151 8 al | + x li animistsb of noleivib offerlinve a20 2. Laura owns and operates Aunt Linda's Pecan Pies. She has learned that her profits, P(x), from the sale of x cases of pies, are given by P(x) = 150x - x2. a. The company will "break-even" when the profit is zero. How many cases of pies should Laura sell in order to break-even? (Solve for x when P(x) = 0.) Write your answer in a complete sentence with proper grammar and correct spelling. P( x ) = 0 O = 150x -* isgo Welliw sonsthea atelamos Laura Should sell 150 cases o O = x (150- x ) Pies in order to break - even. = 0 (F ) [ x = 150 (T) b. How many cases of pies should she sell in order to maximize profit? What is the maximum profit? Write your answer in a complete sentence with proper grammar and correct spelling. .clolost isenil to fouborg is as nolfonut limonvlog sri efnWvMath 1314 Lab Module 3 luboM ds.) page 3 3. For f(x) = x3 - 7x2 + 8x + 16, holo bris villamia how lie worla empidong gniwolfol of to lose Biting hiw lief test 935 publied b do got so mond biswad vileathav nwound a lied man a. Find f(10) using synthetic division. ed off to (feel ni) beonatelbert brossa leg igot SA to diga sialgmos s ni dewere woy onW Sbougie er exide lied artesob ebnobes vram wod jona b. Is 10 a zero of the function? Explain in a complete sentence with proper grammar and correct em spelling. to idien mumisin ers al fanW Aripied momixer all noseTuned ant iliwinsaw prillege foonog ons ism mp egong liw saneMes sfelgmos Is nietswans wow c. Use synthetic division to determine if x + 1 is a factor of f(x). mon ,(x)9 stilorg end fadi bemeal earl aria .egidineed a sohiJinUA estsisqo bas anwe bus x - koat = (x)1 vd havin sis ,esiq to 20360 y to slee ari musd bluorie asiq to esaso vnsm wol mies a lilong erit nerdw 'neve-issid" lliw vnegros enT s stelamoo s ni owens woy sil (.0 = (x)9 nerw x or svice) neve-Nsaid of 10b10 nillee grillage lostloo bris ismmeng 18goiq rhiw eoneinga d. Is -1 a zero of the function? Explain in a complete sentence with proper grammar and correct spelling. munixem ent al tedW Chong scimixe 1 of jobio fillsa era bluoria esiq to eseso ynam woll d e. List all of the zeros and their multiplicities of the polynomial. s ni dewans mov sthW finonq f. Write the polynomial function as a product of linear factors