# Document 10502999

```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
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-
r A- .r
(c)
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\
(0,-r)
J
s
t
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AK
rt
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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
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(c) What is the life expectancy of the car? (i.e. When is it expected to be worth nothing?)
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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?
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(b) Which costs more per item to produce?
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s P.7o1xn tr r n-ltt+\
(c) Which item costsmore to sta,rt up?
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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
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(d) If they produce 5000 bottles of sauce,what is the compa.ny'scost? Revenue?Profit?
: 0.5(szoolesa;
r., * *._,@
C(sooo-)
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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?
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= ftl,ooo+/vtwq'&quot;J
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lo o o= 1 4 .td Sl{ + A' t1 4 3
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a = 4i. {11+lo
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6. The table below
zo a-bo1^*
{MrU%,}o
data on the
i^/-otg
(&lt;tt ur-e-\&lt;
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 &lt;
6.25
gW&quot; dllrv.t^n=flJ
Find linear regressionmodels for this data and use them to predict the(quilibrir''&quot;
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7. Use the following graph of a function / to estinate c or 3r. Some problems may have more than
,
@) u: f_r ) &quot; 6
x=t , x=-{
(u)a: /(c)
(c) /(r) &gt; 0
a-'\t x vv-t^'4&quot;/k'^'l&quot;ick'ltr)Vo
a
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8- Find the domain of the.following functions:
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e -l\x&gt;ro
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x L- a
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t o l 9 (r/: C _ A cz+ ro r \
(A- a' (
ba O
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x(rL -8x + t5\--Q
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J
x--o
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X--5
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X=3
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9. For the following functions, find:
i. t@+h)
ii. f(a+h) - f(a)
.-. f@ +h)- Ib)
n
(.) /('): j&quot;
I
f ca+t^;-- (a-+n)z
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:
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h
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0\ *[x)-{r;
= \$ - @+a\
f (0&quot;v,,)
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h
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```