11. Interpreting Nonlinear Expressions

Interpreting nonlinear expressions

1. Ben Ben Frank rank is an elec electr tric icia ian n who who inst instal alls ls ligh lighti ting ng fxtu fxturres. es. He charges (in dollars) his clients15h clients15h+40f  +40f  where  where h is the numer o!  hours worked and f  is  is the numer o! fxtures installed. How much does Ben Frank charge when he works " hours and installs # fxtures$ fxtures$ %orrect answer& ' 45

*. he

ex,ression

!or

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the

sur!ace

area

o!

a

cue

o!

side

length s is s s*. -hat is the sur!ace area o! a cue with side length %orrect %orrect answer& *"* s/uare s/uare units

. ric

owns

and

o,erates

the

3 2

 units$

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Hot

Ham

!ood

truck.

he

h gies the cost burgers and h hot dogs. ex,ression .*5b .*5b+* +*h -hat is the cost o! 4 urgers and  hot dogs$ %orrect answer& ' *5

leel&1

4. he he ex,r ex,res essi sion on 1* 1*g g gie gies s the the num numer er o! kilo kilome mete ters rs a car car can can trael using g liters o! gasoline. How !ar can this car trael on 5

1 2

 liters o! gasoline$

%orrect %orrect answer&  km leel&1

5. he ,rice ,rice o! a isit isit to the dentist dentist is calculat calculated ed accor according ding to the !ormula 50+100n 50+100n where n  is the numer o! caities the dentist fnds. 2n 3our last isit to the dentist * caities were !ound. -hat was the cost o! 3our isit$

%orrect answer& ' *50

leel&1

. sh c ( q )= 2 q + 155 √ q + 2,000  com,an3 manu!actures ookcases. ookcases. he !unction aoe gies the cost %(/) in dollars o! ,roducing

q

 ookcases. -hat is

the fxed cost o! ,roduction e!ore an3 ookcases are ,roduced$ %orrect %orrect answer& *000

leel&*

". he !ollow !ollowing ing e/uati e/uation on shows shows the height height h in meters aoe the ground o! a !ootall t  seconds  seconds a!ter a ,articular kick. 2

h =0.3 + 5.5 t −4.9 t 

-hat was the height o! the !ootall at the moment o! the kick$ %orrect %orrect answer& 0. meters

6.

leel&*

B ( n )=2

n

 inar3 code word o! length n is a string o! 07s and 17s with n di digi gitts. For exa xam m,le le 100 001 1 is a i in nar ar3 3 co code de wo worrd o!  length 4. he numer o! inar3 code words B(n) o! length n is shown aoe. 8! the length is increased !rom n to n+1 how man3 more inar3 code words will there e$ . * B.

2

%.

2

9.

4

n

n+ 1 n

%orrect %orrect answer& B

#.

F ( t )=1,500 ( 1.045 )

leel& *

t 

 he !uture alue alue F (t ) ) o! an inestment a!ter t  3ears  3ears is gien 3 the !unction defned aoe. -hat is the initial alue o! the inestment$ %orrect %orrect answer& 1500 leel& *

10. R ( q ) =−0.31 ( q −260 )2 + 18,500  shoe manu!acturer determines that its monthl3 reenue R(q) in dollars is gien 3 the !unction defned defned ao aoe e where q is the numer o! ,airs o! shoes sold each month. -hat is the maximum alue o! the com,an37s monthl3 reenue$ %orrect %orrect answer& answer& 16500 leel& *

11.

 P= $ 150

(

1−

( ) 1

1.03

0.03

10

)

 he e/uation aoe gies the ,resent alue alue P o! an inestment that ,a3s the inestor '150,er 3ear !or 1010 3ears. he ,resent alue is the dollar amount that is e/ual to the series o! !uture ,a3ments. 8! the ,a3ments are changed !rom '150 to '"5 what is the e:ect on the ,resent alue P$ . the ,resent alue sta3s the same B. the ,resent alue is haled %. the ,resent alue doules 9. the ,resent alue increases 3 ; %orrect nswer& B leel& *

1*. P ( q )=−0.01 ( q−250 )( q− 80)  he e/uation aoe gies the ,roft ,roft P(q) in dollars earned 3 a cu,cake aker3 when q cu,cakes are ,roduced. ,roduced. -hat is the est inter,retation o! the numer 6060 in this context$ . 60 is a numer o! cu,cakes !or which the ,roft is e/ual to '0. B. 60 is the numer o! cu,cakes that corres,onds to the maximu ,roft. %. 60 is the the nume umerr o! cu, cu,cak cakes that hat cor corres,o es,ond nds s to the the minimum ,roft. 9. '60 is the maximum ,roft ,roft in dollars. %orrect %orrect nswer&  leel& * 1. mehmet ex,erimented with the numer o! grams (g) o! sugar that would dissole in a s,ecifc olume o! water at di:erent tem,eratures. tem,eratures. He modeled his results using the aoe e/uation to re,resent the numer o! grams m o! sugar that dissoled when the

water was x  was x  degrees  degrees %elsius (?%). -hat is the est inter,retation o! the 161.5 in >ehmet7s e/uation$ . 8n his ex,erime ex,eriment nt a maximum maximum o! 161.5g o! sugar sugar dissoled dissoled in the water. B. 8n his his ex,er ,erimen iment t 0g o! sugar ugar diss issole oled d when when the the water ater tem,erature tem,erature was 161.5?%. %. 8n his ex,eriment when the water tem,erature was 0?% 161.5g o! sugar dissoled. 9. 8n his his ex,er ex,erim imen ent t the the maxi maximu mum m num numer er o! gram grams s o! su suga garr dissoled when the water tem,erature was 161.5?%. %orrect nswer& % leel& *

14. T (r )< )<

72

r  he @ule @ule o! "* estimates the time time T (r ) ) in 3ears needed !or an inestment to doule when the annual interest rate is r ; ; as shown in the !unction aoe. -hich o! the !ollowing is the est descri,tion o! the numer "* in this context$ . "* is the time time needed !or !or an3 inestm inestment ent to doule. doule. B. "* is the numer numer o! 3ears 3ears needed needed !or an inest inestme ment nt to doule doule when the annual interest rate is 1;. %. "* is the maximum maximum numer numer o! 3ears it can take take !or an inestment inestment to doule. 9. "* is the numer numer o! 3ears 3ears needed needed !or an inest inestme ment nt to doule doule when the annual interest rate is *;. %orrect nswer& B leel& 

 x )< 15. A 15. A(( x  )< =

1 4

 x =*5)  ( x  =*5)*+*5

 he area A area A(( x   x ) ) o! a rectangular enclosure enclosure that can e made !rom a limited amount o! !encing is shown aoe where x  where x  is  is the length o! one o! the sides o! the enclosure measured measured in !eet. -hat is the maximum area that can e enclosed$ %orrect nswer& *5 s/ !t leel& 

1. -ilma created created the !ollowing !ormula !ormula to model the distance d in inches aoe the Aoor o! her um, a!ter t  seconds  seconds had ,assed. d