I

l\t
Chapter 4 Word Problems
Algebra 2 Pre-AP

'r'l

-^

- so8

i1 jli ll

i:.

i l!! i!
',i

t, ,il

'j

i.

Nome

j

)

t,

i ."'i ' i

ti'f f

:

i'
1.

The
P

:

profit

for o compony thot produces ontivirus and system utilities softwore is
+t40x - 250,000 where x is the number of units qo-!d,'lflh,gt soles level will yield o
-0.0002x2
P(in dollars)

moximum prof

2.

it?

,1.

' ., .

.

i-}l

;I{,.1

o.
b.
c.

J. t X \..11

4,1.',',,'-^r.'t

J

:g

J

.

ii'''

Use the model to opproximatethe percentage of totol income thot on indivibuol who is 45 years n,,, of age spends on heolth core.
'i i
At whot age is the percentage of income spenf on heolth care !O"/"?
'.. ) ( ;-; l
Bosed on the groph, whot hoppens to the percentoge of income spent on healfhcare os individuols

aoe?

..:.

i'." ir

t

ra",fu,"a |,F;j.o

4.

hieh.

o.
b.
c.

k

-fn

."

/

i)*

i

-"rinitiol velocity of 64 f eet per second fnom o plotform 80 feet

,

Write on eguotion thot models the poth of the object.
When will the object reoch o moximum height?
How mony seconds until the object hits the ground? l -

r

"\

't , -

'

{l,Y-,r', l-')t),'rr
'(l)
DeeSidehosopigthotpiesentlyweighs2OOfounds.

it r

Shecouldsell itnowforapriceof $l.4Qper pound. The pig is goining 5 pounds per week, ond the price per pound is dropping 2 cents per week.
o.
b.

,

on eguotion for the totol worih of the pig o's o functiori;of weeks.
When should Dee sell the pig to geiihe moximum omount of money f or it?

Write

Luke and Leia are tropped in o room on o space

wide, but the length is decreosing ot o rate rate of 3 meters per minufe.

o.
b.
c.

stotion. The room is 20 melers long ond 15 meters of 2 meters per minute, ond the width is increosing oi o

Write on eguotion fhot relotes oreo (y), in sguoremelers, ond time (t), in minutes.
Does the area of the room reoch o maximum for o positive volue of t? Tf so, whot volue of
;.'
nof, how do you tell? ' r".
When will the area of the room be zero? t *i

1l

"-*."'-'J

I

"t/

)tl

16.

L-

Thefunction H(x)=O.OO4x2 -O.lg7x+5.406 models thepercentageof total incomethoton individuol who is x yeors of age spends on heolth core. (Source: Based on doto obtoined from the
Bureou of Lobor Stotistics.) "7r'' i'
.

5.

'

I

A farmer with 2000 meters of f encing wants to enclose o rectangulor plot thot borders on o stroight highwoy. If theformerdoesnotfencethesideolongthehighway,whotisthelargestoreothotconbe

enclosed?

3.

-.*

l,

,",):

-

.i

,."

|

i.;
-

t? Tf
1a, 1,,:

,

7.

A science center hos o rectongulor porking lot. The science center wants to odd 18,400 sguore feel to the area of the porking lot !y expbnding the existing porking lot os shown.
:;

-rt

i

\ I{

\' '('

'

p"1"1-

3?0 ft

-------j

T

Lf

r,)"i;,';,

I 'f .j i: \

150 ft

I
I
o.
b.

Write
Solve

\ tif

thot could be used to solve to find the volue of x. the eguotion from port o. By whot distonce x should thelength

) ;'; 'r.

-

,'-:,

il

:" i

on eguotion

ond width

of the porking

lot be expanded?

Regression Word Problems
8.

Suppose thot you ore on actuory for F. Bender's fnsuronce Agency. Your company plons to offer a senior citizen's occident policy, ond you must predict the likelihood of on qcqidq.nt os o f unction of the driver's age. From prevrous occrdent recot 'ds, you f ind the follo$rinq inf dent tolloping informotion:
U, -\\ ase Qf yeors)
20
30

40

Accidents per 1-d-0 Million km
Driven
440
280
?oo

I,'
. i\

You know thot the number of occidents per 100 million km driven should reach o minimum then go up ogoin for very old drivers; theref ore, you ossume thot o guodrotic function is o reosonoble model.
o.