coturiahr ?all 2007 A^y
CoIUN
Week in Review # 2
Sections 1.2, 1.3, and 2.1
Things to know:
o How to work with lines: interpreting slope, finding linear equations
o How to perform linear regression on your calculator
o How to work with functions; definition, evaluation, graphical information, finding domain and ra.nge
r How to find cost, price, revenue, and profit functions
1. Find an equation for the following lines:
/,. @rl\
(a) The line passingthrough (-2,3) with a y-inteicept of 1.
-a
m= r-3
oi-.l -- 7
-- -l
(b) The line with r-intercept -4 a.udslope t.
(-4ro)
t$-'Z
I-e:%rx++)
-
r A- .r
(c)
{-"
Xlt o
\
(0,-r)
J
s
t
$-i
aq'
AK
rt
-!
'-5
il
\-- zx -l
Two yea.rsafter purchasing a new car, it is worth $23,400. Three yea,rslater, it is worth $5400 less.
(a) Assuming linear depreciation, find a linear function that models the lralue of the cax r years
a,fterit's driven off the lot.
(a,ta,+oo)*=*
X- 5aa':
5, w!6ib
= tryn
L\-27 loo= -tsoo(x-a)
,.
. g= -'{;ii
i'zuco+z?+u J
tD,, rlow mucn was tne ca,r worln Drano newf
-t(00(o)+a1ry2
00oJolh.r
-^1
--:l:vlo
x?o
r' L'l---ltt)ox rL1\oo)olVrs'
' urar, * i5 qAt {v,u'trx
a,fc.
t^)a'/)
t4t'5 c,^^.
tl ,,r7,/\
prn0r, .L
4
pura"b4.X4
(c) What is the life expectancy of the car? (i.e. When is it expected to be worth nothing?)
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o
rx
t,oo)
F
i
f
-_t80ox +??00o
21ooo
t42 - WeL-iERei*
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3. Let C1(c) = 0.35o+ 2450be the cost of producingz doodadsand Cz(c) = 0.20c*3500 the cost
of producing r trinkets.
(a) How much doesit cost to produce3000doodads?3000trinkets?
= o,as(aooo)
t, Qooo)
+14sD=EaG
=@
[10*07 -- o'rc(aooc\*'z'{oo
(b) Which costs more per item to produce?
cos+ (o,as 6zvd.oada/ vs.
{^AtbA
.lao6v
AorLads'
s P.7o1xn tr r n-ltt+\
(c) Which item costsmore to sta,rt up?
r*-0afz4stt 'nlNd
cos+s
'
\'6
hpd
$Xu>
-W\ttlr+s
*nt
CosN<
dool'als
Bevo BBQ, Co. determined that the rariable cost of producing their BBQ sauce is 50 cents per
bottle and the fixed costs are S250. They charge $5 per bottle of sauce.
(a) What is the compa,ny'scost function for thel BBQ sauce?
C(*)= 0,5xt25D dotlcts1w\'oo t-is +l'u*%bot4lA
praLuuA
(b) Their revenue function?
K[r)= ot' lol]at\ ''rtL{ / is Ir $b'trdzg
(c) Their profit function?
P(0'[/xl-cU)= 5r -(o,tx]aso)
p,rf=',t,L; i'b ;,t; (s,u,tra)
x ic*Sbntlt s prut,nwl
?.XA
(d) If they produce 5000 bottles of sauce,what is the compa.ny'scost? Revenue?Profit?
: 0.5(szoolesa;
r., * *._,@
C(sooo-)
---5G0Do\
K(5rlcD)
le"Ltd
Pt ) =(4sD//o)-c(saD)
-- Asan - L1m
ttt2 - w*i6&ais
@crfi{,ht Fou 2oo7 Atu! coltn'
\|
3
(1
^
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5. The table below gives data for total sales (in thousands)$ f Neuspper XYZ throqh
weeks of the
W6ek
1 2 3
4
6
8
10
Total sales(K) 33 62 98 121 174 235 307
the first 10
Find a linear regression model for this data and use it to arxswerthe following:
(a) During what week will total sales hit one million dolla.rs?
"rl.>&/,.Lx \5 'l't4 * qrwczas bt{\ LL-br'btt\^i'5 ud'dr
'ao5--tooo
= ftl,ooo+/vtwq'"J
$lrooo,ooo
lo o o= 1 4 .td Sl{ + A' t1 4 3
(b)wl.t
th"i,*e"ktffi-l
"""
fl\[N0\d{r/ttd*
%
q q 1'tos?-- Lq @eTl
1ona4:tirue.in"j
a = 4i. {11+lo
U* "'('
clalnqz',5 LD?E!
r tt?(1,
vo
v^. 2q, VltL
6. The table below
zo a-bo1^*
{MrU%,}o
data on the
i^/-otg
(<tt ur-e-\<
at which z items will be either demanded or suoolied.
50 100 150 200 250
price - dema.ud$) 27
23 20 r 1.c
price - supply($
2.5 a <
6.25
gW" dllrv.t^n=flJ
Find linear regressionmodels for this data and use them to predict the(quilibrir''"
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=-0'04tx +7q3 d'odu,ts.Yn*,
F
$l4oywrnlu ff ilemsdm!'^ftd ,
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N4'41 x
! ( ' et ' t v ( P I 1
in)r'.
S{ore
v'rJ
/'ot'!rl W'ru'YL;+
t wl^ut x ts
P.=O.024x+ 0'15
Y--V.vrr,'
Wwrytubry
W Ulwltflr t0 h^/
poi/I*.
iru{,r:cctru}r
(ry*iJ,\aisa
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7. Use the following graph of a function / to estinate c or 3r. Some problems may have more than
one answer.
,
@) u: f_r ) " 6
x=t , x=-{
(u)a: /(c)
(c) /(r) > 0
a-'\t x vv-t^'4"/k'^'l"ick'ltr)Vo
a
Jl*,n
[t,rl]
tt,'[U
8- Find the domain of the.following functions:
(u)f("): Vi=Ti
6tr-Yd-attP
a .aDl
e -l\x>ro
-ltxz -t5
(-^,*]
x L- a
<_.!d
%=3
k-pL ?)
t o l 9 (r/: C _ A cz+ ro r \
(A- a' (
ba O
YJ-Lr'+,sv = o
x(rL -8x + t5\--Q
X(rc-sXx-5)? o /
J
x--o
X'? - rc
X-f=O
X--5
?Arf O rn'@
X=3
/
(-
fuwfutwnltftir,5s
ilol ir,ltrtiuconbeilltz
, t--b rnoltotdl,tl.ou. =O
x.*5>0
bue
f"ca*Y@
?,u,,
xzb (?,5)V(<,a)
Ut+>r1
IL
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9. For the following functions, find:
i. t@+h)
ii. f(a+h) - f(a)
.-. f@ +h)- Ib)
n
(.) /('): j"
I
f ca+t^;-- (a-+n)z
')
,t
IL
- *
@-I+x\L
:
aL(a+tY
- @'n^t
a-'(a+|"\'
+*)
&L- (aa+uv,
7@+h)z
n 7 - d -- a a - h
.
-\
tL
? t "+ h ) z -JaV-nx
L,')
.[(a+h)-lr")
---r-
h
'^laV'-*
=
L
\mfuk)i.
)
--k(t"-h)
l,aLta+t')t
h
-r^:!_
nL(a+h\L
0\ *[x)-{r;
= $ - @+a\
f (0"v,,)
,)
frorr,l-lta\ =
- tfFo
b- *- l
,,)lgujet=€g
-
/
r--\
J6 - a L \ /
h
tl
/\
rwda'o'rl '
-fhoit o P"n $11a
7* -v -7 Y*
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