Math 1090 Final Exam
Fall, 2014
Name
Date
Student id#:
Instructions:
•
Please show all of your work as partial credit will be given where appropriate, and there may be no credit
given for problenis where there is no work shown.
•
All answers should be completely simplified, unless otherwise stated.
•
Make sure all cell phones (and all other electronics that can connect to the internet) are put away and out of
sight. If you have a cell phone/other electronic device out at any point, for any reason, you will receive a zero
on this exam.
•
You may use a scientific calculator only. No graphing nor programmable calculators allowed.
•
You will be given an opportunity to ask clarifying questions about the instructions within the first fifteen
minutes of the time the scheduled final exam is advertised by the University to begin. The questions will be
answered for the entire class. After that, no further questions will be allowed, for any reason.
•
You must show us your U of U student ID card when finished with the exam.
•
You can ask the proctor/instructor for scratch paper. You may use NO other scratch paper. Please transfer
all finished work onto the proper page in the test for us to grade there. We will ntI grade the work on the
scratch pages.
•
You are allowed to use one 8.5x1 1 inch sheet of paper (front and back) for your reference during the exam.
STUDENT—PLEASE DO NOT WRITE BELOW TillS LINE. TI lIS ‘TABLE IS TO 1)l USED FOR GRA1)ING.
2
#1
3
#2and3
4
#4
6
#6
7
#7and8
8
#9
9
#loand 1!
10
#12
Raw Total (out 01’ 200):
‘l’otal Percentage:
• (a) (12
Graph the region of the plane (the feasible region) that satisfies the following inequalities.
xO
1’ 0
2x
y 3
Make sure to label the vertices of the region and shade in the desired region.
points)
y
2
IO—
®
(‘
()
I_1_
LC
L’7 I
—
rrr
——-4-
-
-:-
,
-:
r
L::
—
(
L
H: :L :E : t: : E
2\ :/D-27
=
—
=
—
11111
L
—
=
EE
—
L
—
—
=
11111
_L_ .L_
I
I
LL_L_L.1_L_1I.
t_I__i_1_
(z,
x
)
—,
———
1,11111
I
————
I
I
I
“I
‘6;
7’ch
)
1
(u
iT(b) (6 points) Find the maximum value of the objective function P
(above), and also find the point where that maximum occurs.
*
,CLL”
1
Y
Sb-)
fr7V
::-
c(c)rL
5x
+
4y subject to the constraints in part (a)
4;. /‘;
)
Mt..
C)
‘)2’
:22-
/ 7
)i3
‘
t
Max P-value:
-
point where max occurs:
/
I
‘
2
/
2. (12 points) Find the equation of the line that passes through the point (4, 1) and is perpendicular to the line given
by equation 2y + x = -4.
()
-7
Line:
,-j
‘ive line in slope-interceptform.)
3. (12 points) Solve this system of equations, using any method youd like.
I Ox + y = 6
3x + y + 2z = 3
2x—y—2z=2
2
-t/X
2
-
)2
2?Z
2- I2-?
/
I
,,\
LzLL
2 ?(,) -3
Solution:
I
I)
3
4. (ise these matrices to compute the following, or explain why the computation cannot be done.
4],
B={
(a) (6 points) 213
—
c=[
3
C
-
/
L
-
oi
‘
I
Answer:
(b) (6 points) AC
2
c)
0
2
r7
Answer:
(c) (6 points) BC
,
Answer:
4
t1
-
12.
‘1
27
5. In order to sell x watches, the company will sell them for (20—x) dollars each
is C(x) = 8x 13 dollars.
.
The total cost to produce x watches
—
(a) (6 points) Find the revenue and profit hind
ionS.
Revenue Function: R(x)
Proflt Function:
—
P(x)
-
/3)
L
-
/ ./
(b) (6 points) Determine the number of watches that must be sold to break even.
-12
-
(.+i)(-i3)
x—1
--
x
=
1’?
in order to break even.
(c) (6 points) Find the number of watches that must be sold to maximize profit.
/
x
=
(d) (5 points) Compute the maximum profit.
-÷/2/
maxprofit
5
to maximize prolil
6. Answer these questions.
(a) (6 points) I. se logarithmic properties to condense this expression into a single logarithm.
+4 Iog3
og
5
l
1
logx—
y
-
/7
3
5
+4 1og
logx—log
y
5
(b) (12 points) Solve this logarithmic equation.
x+ i)
(x)+Iog
—log
(
4
///
3(
7
0
/1’
Lf
K
.>) V
-
Solution(s):
(c)(12 points) Solve this exponential equation.
x-- x2
=1
e2)
2J(
)cH
t-’
1))
)(—
Solii1ion(s —
6
—
/
7. (15 points) A company wants to remodel their office five years from now. The work will cost $90,000. They decide
to invest money at the end of’ each month in a savings account earning 6% interest, compounded monthly for the next
live years. I-low much will they have to invest each month to have enough money for the remodel? And, how much
interest will they earn over that 5-year period?
Formula used to compute monthly deposit amount:
4
i
f..
j Ot
—
For this formula (the one you just listed), list what each of the variable values are. In other words, what are
each of the values you are plugging into the formula you chose?
y•)
(
‘2
C
(If
)2
()OO
Occ)/)
D
Ot
(
Monthly deposit amount:
\D i
ooc)
()
l’34
L
‘
/eJ /2
/L
/ 2, O2
Total interest earned:
-
8. (12 points) Find the present value ofa trust fund if $1500 is to be withdrawn each quarter for 8 years. Assume the
trust fund earns 8% interest compounded quarterly.
J—
Formulaused:
At;
For this fbrmula (the one you just listed), list what each of the variable values are. In other words, what are
each of the values you are plugging into the fbrmula you chose?
7i
,cbo
,q)
(/r)
(&1?
zG2.
z
1
2’
Present Value:
5) _UL.
/
7
/3
I ( )=x and
9. Given functions
g( x)=
2
compute the following.
(a) (4 points) I)omain ofg(x).
-/
Domain:
(b) (5 poilits)
I
_i)
(g of)(x)
\
eli
2
(gcf)(x)
(c)(5points)
(f+g)(i)
1(’)
4)
(f+g)(1)
(d) (6 points)
(A
g ‘(x) (the inverse function for g(x))
—
L7.
L.
g(x)
8
=___
-)
1)
U/
10. (12 points) You lind the car you want to purchase, and it costs $24,000. You plan to use $1l,000 ol your savings
account to pay a down payment. Thus, the amount to be borrowed is $13,000 at 2.4% interest compounded monthly
frr 5 years. I low much will your monthly payments he?
Av
loniiula used:
For this formula (the one you just listed), list what each of the variable values are. In other words, what are
each of the values you are plugging into the formula you chose?
?
)cO
/2
7o
,,
(1-
(/
/L)
(
C)
) )
Monthly payment:
II. (12 points) Jens wants to save up for a trip to the Netherlands when he graduates college in Ibur years. lie
estimates that the round trip plane ticket will cost $3000; in addition, he wants to have another $2000 for living
expenses while lie’s there. In order to reach his goal. he plans to deposit one lump sum amount of money now into an
account earning 5.4% interest, compounded monthly. How much does Jens need to deposit into this account to reach
his goal?
‘C
Formula used:
For this formula (the one you just listed), list what each of the variable values are. In other words, what are
each of the values you are plugging into the formula you chose?
?
K,OOC
(i
o
&
ooo p(
/) 1 2
/
/
/
I)eposit amount:
9
.
2 (x + 2)— 1
y = log
2. For the function
(a)
(4
points)
State the domain of the function.
“,
N
-
cI—
?.‘
>
Domain:
that
this
graph
through?
(b) (6 points) List two points
goes
y=
2
(r2)
O
/
-HO-i
(2)-/ I-(
e0
)C)
—
1, i)
(O c)
and
Two points on the graph:
(c) (6 points) Graph the function. Make sure toe1ehr1y show at least two points the graph goes through.
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