Iml~~ ..- ""', Most "Pcope ~I i \! t'(x) X $480'~'~' = $12,000. ea ~ I..U pi. 4'la. F X[1111 Ihf. .-b-w. $Lt<60. cam. ~~40 ~160 s IdO $60 \00

Size: px

Start display at page:

Download "Iml~~ ..- ""', Most "Pcope ~I i \! t'(x) X $480'~'~' = $12,000. ea ~ I..U pi. 4'la. F X[1111 Ihf. .-b-w. $Lt<60. cam. ~~40 ~160 s IdO $60 \00"

Andra Carson
5 years ago
Views:

ntroduction to Rational Functions ACTVTY 27 Planning a Summer Camp Lesson 27-1 t Learning Targets: Formulate rational equations that model real-world situations Graph equations on coordinate axes The

1 ntroduction to Rational Functions ACTVTY 27 Planning a Summer Camp Lesson 27-1 t Learning Targets: Formulate rational equations that model real-world situations Graph equations on coordinate axes The finance committee of a nonprofit summer camp for children is setting the cost for a 5-day camp The fixed cost for the entire camp is $2 400 per day and includes things such as rent salaries insurance and equipme nt An outside food services company will provide meals at a cost of $3 p er camper per meal Campers will eat three meals a day \ Fee per Camper r \00 '200 '4 ht 4 HJ ' \dooo ;)s r '- \ rhl l U lal 'i 'v' - t ''' ml ea cam \000 x ----?l'l5 $480''' Most Pcope i \! n 4\ne Cllvrq:> t Yjr Dtl ' ti''ltft1t ('''i'- Of 4'la \(1000 _ C ---- $ aw Use the patterns you observe in the table to write an algebraic expression in the last row when there are x campers c JLfyo u have a camper ;:>) th 15 r 'H cc re -tyy man campct s do $60 ' --' vl -- 't 50 p U pi b Complete the table below to determine the fee per campe r that will iy) ( guarantee the camp does not lose money OU Q as -<!' ' = $12000 $Lt<60 :11 t \'; 1 nitially the committee decides to calculate camper fees base fixed cost of the camp alone without meals for the campers dnt a What is the total fixed cost for the five days? Number of Campers c'c B tl T L1\ rt J' 11 a -b-w 11 u As a nonprofit camp the camp must cover its costs but not make any profit The committee must come up with a proposal for setting the fee or each camper based on the number of campers who are expected to att end each week / F X[1111 hf SUGGESTED LEARNNG STRATEGES: Marking the Text Summarizing Paraphrasing Create Representations Look for a Pattern d YOQ )( 5 'll' t'(x) X Activity 27 ntroduction to Rational Functions 417 l-

Lesson 27-1 ACTVTY 27 continued c Using an appropriate scale make a graph showing the relationship between the fee per camperand the number of campers in attendance - MATH TP 4 M+- i--+-+-+-'-+-+-!

2 Lesson 27-1 ACTVTY 27 continued c Using an appropriate scale make a graph showing the relationship between the fee per camperand the number of campers in attendance - MATH TP 4 M+- i '-+-+-! '---c You can use the values in your table to help you determine an appropriate scale for a graph E >'C i-i--f--j oo i-+i--+-4: f+ i - OO ' Number of Campers d Write an algebraic rule for the fee per camper as a function of the number of campers in attendance f(x}= QO v: represen+s numtej( of CoY'()peKS f(x) (epresents -the fee Dercamper 2 Describe the features of the graph in tem lc d screre po\n! -the B(phrs aecreas\n3- Q n X \ V wases )-the -flanc;hm rcaches zero d tos\-ne \'nexlo AS X <A?0'COcnes -zero {he -func:ho'l'l \nases 3 Reason abstractly Based on your work so far is there a minimum camper fee not counting the cost of meals? f so what is it? Explain -f(x) 0 d) T10Ne'JeK:!he GOn'()ct 'ho\d el'{) \rf\n\te OimOLAnt cg\ Y( GhC omo\\1/it 'NOUJlQ be 9:xJ carnpet's 'N'n rneo:ns 'n-!y) \ VYlU vy1 WO\JJ) d k1e f OOQ :: \u < as x-;' co -+ -r {ch or -tjtto fee Check Your Understanding 4 What is the fee per camper if there are 2000 campers? 5 What relationship exists between the number of campers and the fee per camper? 6 Describe the domain and range of the function in the context of this problem -t--+--t-+-t---t t--i ( )\1OCQ_:: S6 'lux) j----j 418 f:s wosej X \n (:\ CXeCA ses fee pif ca Mathematics Algebra 2 Unit 5 Radical and Rational Functions

3 t; fdi Co ii!; Lesson 27-1 ACTVTY 27 i ;< # continued c 7 The function developed in tem 1 did not account for meals Campers t;jt 51 eat three meals per day at a cost of $3 per camper per meal The committee must determine a function that includes the cost of meals when setting the fee per camper a What will be the total cost for meals per camper each 5-day week? vtxs==- $ 3)( 45 mead s z: q - X 5do! S = $ 45 / b Complete the table below to determine the fee per camper that/ will guarantee the camp does not lose money Number of Campers Fixed Cost Plus the Cost of Meals Fee per Camper 3\as as =-Sc \-aopo 4-t15(a5) 25 $\3aC) \soco [sd:j 50 ' d85 - O5 100 \6500 l (OOO ) J!l <:: <;; ' U ' U 0;200 bil i f '1 ' t t 100 LL 3aO 'llo &D f TH dj 'M$ t-r- _ ; 1:0' '10 \ '400 N Q! Number of Campers d Write an algebraic rule for the fee per camper including meals as a function of the number of children in attendance rex) - laooo + l\ 5><_ >< 'W'nQre 'X \ S -Bre tfi ccwyeys ca'0a -ten f ldo 200 w- f- Q o '0' ' ' o ' ' -0 : \S fee ; < Q E CO 5DO : X -0 i- i c Using an appropriate scale make a graph showing the relationship between the fee per camper including meals and the number of campers ''e 57 rooo+ 4 X \aooq+45x x - Sl)oOO 1000 Describing the behavior of rational functions as they approach horizontal and vertical asymptotes provides an introduction to:a more formal study of limits that will occur in calculus' '; \ ' Gq 3L-1S00 '-'AP' ' C; ' 500 atl t= l S 75 5 colf'{) Activity 27 ntroduction to Rational Functions 419

$Explain your reasoning a\- \ st $45 ssre eo %'e fl' wsts -tnljnct \by :h\jch n9 $to J oro '0'1 -\:he of ca5 9 How does your answer to tem 8 differ from the one you gave for tem 3?$

4 Lesson 27-1 continued 8 Based on your work so far is there a minimum camper's fee? f so what is it? Explain your reasoning a\- \ st $45 ssre eo %'e fl' wsts -tnljnct \by :h\jch n9 $to J oro '0'1 -\:he of ca5 9 How does your answer to tem 8 differ from the one you gave for tem 3?- -\ern e \h eludes\:hp So -\:he \r'nln (mum \X)Sb\b\C CDst of \s) tee chad Check Your Understanding 10 What is the fee per camper if there are 2000 campers? Why is your answer different from what it was in tem 4? 11 Describe the domain and range of the function that includes the cost of meals in the context of this problem 12 Describe the difference between the graphs in tems c and 7c LESSON 27-1 PRACTCE A new start-up company is going to produce cell phone chargers The fixed cost for the company is $800 per day which includes things such as rent salaries insurance and equipment The total daily cost in dollars to produce x chargers is C(x) = 4x Evaluate and interpret C(OO) and C(100) Write an algebraic rule for finding the average cost per charger 15 What relationship exists between the number of chargers and the average cost per charger? 16 Make a graph showing the relationship between the average cost per charger and the number of chargers produced nclude data points for producing and 1000 chargers 17 Make sense of problems The company has determined based on warehouse space equipment and number of employees that the maximum number of chargers they can produce in one day is 6000 Given this information describe the domain and range of the average cost function 420 Springfsoard' Mathematics Algebra 2 Unit 5 Radical and Rational Functions

5 Lesson 81-\ t>dlce Werre ddo Wtllt'jOuJeY1Q\Nl ' F Xtrl cost- :=$800 (lt ' _ - _ C(x) :; 4-x + BOA --_' ' 1- Yi duc - - =- {5()\_th\\t'co!_\U-PQ cha X -= Jlumber- of chayg:ys c'(\ol- -and d0o- _ ' \ _--'-----=----_ (\00)-: li(\oo; _l2qq j / To rp'{oduce \00 'ChQ{gefS_ i:he dell\y _cost OQQ _ C(OD) = Y(lOO)+800 -'200 _$ll _ 100 \00 \00 \\'e oblage- cosr -tv4>voduce ioo_r@cfg 1s_$lL _ -Fe - _ '_ 4)( +Boo- - - x L A \S_-hum'oeY: eft _dco'l'@erb\jr)crease _ OJleJQf!P- cost- -pev ctaavger 'NJ U d '--- _ = t6- _ AJfJ(ac;r;Ws+peicFoeY -_ - _--_-_-_-_-_- S(L -i=_o \00 $ld :'25' o-----!8_ b_ - - ' $ 533 -O _ - r-'----t- goo $ S00 \j _ \000 _y:o o 700 '100 boo \l\aoroe-r efrg

6 4 \3 The :t- r'- 'j r- ---''l ; '

ROLLER COASTER POLYNOMIALS

Math 3 Honors ROLLER COASTER POLYNOMIALS (PART 1: Application problems small group in class) (PART 2: Individual roller coaster design) Purpose: In real life, polynomial functions are used to design roller