Prof Luong Le
STUDENT’S NAME_____________________________
ID_____________________________
COLLEGE OF THE CANYONS
SUMMER 2021
MATH 104
EXAM 4
FORM A
PART 1
1) Please, do not discuss the exam with others while taking it.
2) Neither open books and nor open notes
3) Calculators are allowed.
4) Partial credit will be given where sufficient work is shown.
1) (8 points) T-Swift has a balance of $4000 on her credit card charging 0.2% interest per month on her
unpaid balance. T-Swift pays $500 toward the balance each month. Find her balance in 4th month.
100+
0.2'
a, 4000
=
↑
e
recursive
sequence:
an =1.002
92 1.002.4000-500
=
300
-
3,508
=
As 1.002.3,508-500
(an)
=
3,015.016
=
Gy 1.002.3,015.016-500
=
=
2,521.05
$
2,521.03
2) (8 points) A colony of rats in New York City starts with two pairs of mature (one male, one female)
rats producing a pair of one male, one female offspring each month. If all rats mature in 1 month,
produce a pair of one male, one female offspring after one month, and no rats ever die, how many pairs
of rats are there in 7th month?
Eixonaci
za,
F00
=
Mar No
=
Do
Gay Woooooo
=
loam
2
a.
-
=
Do
NoooooooWoWr
und
6
az
as
az
1016
an
26
42
As Go
Az
=4 46
+
an
A1
42
=
pairs
9
27
236196
3) (8 points) Find the sum of the series 4 + 3 + 4 + 16 + ⋯ + 1048576
Formula:
an
G,r(n-1)
=
ai 4
=
236146
en
4(2)
(moszol=enPa)-
en
instal
-
=
v=
3/
1
-(184876)
=n
-
1
en(3,n)
1
=n
-
1
(
I
+
n
11
=
4) (8 points) A truck radiator is filled with 5 gal of water. Now a gallon of water is removed from the
radiator and replaced with a gallon of antifreeze; then a gallon of mixture is removed and replaced by a
gallon of antifreeze. How much water remains in the radiator after this process is repeated 10 times?
2,
az
a
Seq.
9,
Sgallons
Formula:an a, r-
=
(5)(5)
=
(4)(5)
=
=
3
=
4
=
S
=
4/5
=
r
a,0
s(-)
=
Prof Luong Le
STUDENT’S NAME_____________________________
ID_____________________________
COLLEGE OF THE CANYONS
SUMMER 2021
EXAM 4
FORM A
PART 2
1) Please, do not discuss the exam with others while taking it.
2) Neither open books and nor open notes
3) Calculators are not allowed.
4) Partial credit will be given where sufficient work is shown.
Sn=
A. an)
↳+
2
5) (12 points) Find the sum of each series.
a) 5 + 3 + 1 + (−1) + ⋯ + (−33)
1
-
an a, (n
-
↳
28
+
-
-
-
33 5
(n
-
=
Z
S20
1)d
=
33/210
⑧
Szo=(S
+
-
S
-
1)) z)
-
S
-
-
200
-30
=
(n
-
1) - 2)
-
n
-
19
-
1
I
-
1 𝑛
b) ∑∞
𝑛=1 (𝑒 )
n
er t
a=
20
=
=
2
I
2,
2
+
+
et...
+
e
1=
So:r =Sa=
1 8
6) (10 points) Expand the expression using the binomial theorem (𝑥 + 𝑥)
/
My 41 +(8).
-
u
1
*
56
20
x8 8x 28x4 36x4
70
=
+
+
+
70
+
-
28
56
6 2 8 48
+
+
+
+
%.76
(8): =2.5
-
5) s:
2⑧
~
2
(8):i!
8.7.6.s
-
*2.1
8.7.6.
=
70
65
=
S6
1
=(x 2)
(𝑥+2)3
-
7) (8 points) Using the binomial theorem to find the 5th term of
n
a.
()
=
.,
()a
(m)x
ag
( x)) n)) 5))
-
-
2
-
-
-
3
4
-
24
6)24
-
x7
4!
3] (452 5) (-0)
-
=
=
=
=
r 4
3
an-rpr
=
as
-
=
3
+
-
3
-
-
45.2.1
=
(s)(3)
(15)(10)
=
b
x
7
I
24
x7
33
,g
240
8) (8 points) The fixed price dinner at a restaurant provides the following choices:
Appetizer: Soup, Salad, Buffalo wing dip, or Garlic Grilled shrimp skewers
Entrée: Baked chicken thighs, Grilled fish, Lamb chops sizzled with garlic, Honey garlic pork chops,
Stuffed crabs, Crispy roasted duck, Baby beef liver, or Roast beef au jus
Dessert: ice cream, pies, chocolates, or cheese cake.
Ordering such a meal requires a choice from each category. How many different meals can be ordered?
*
128
=
9) (12 points) There are 6 red, 4 black, and 8 white cars in Jay Leno’s garage. Suppose that Jay wants to
pick 5 cars from his garage.
a) How many ways can he pick 3 red and 2 white cars?
cabco,2-:
6.3.4.2
-
-
:t
5
560
=
b) How many ways can he pick at least 4 white cars?
!
Formula:
((n,r)
((8,4)((10,1)
8.7.6.5.4
=
ri(n-r)!
c(8,5)
+
10.a!
↳! 4.3.2.1
8.7.6.5!
I
·
1.
?
10-10
700
56
+
756
=
3:
3.2.1
10) (10 points) Find lim𝑡→0 [
1
1
−
𝑡
𝑡 2 +𝑡
]
~undefined
2
=
simplify
E. ty
t
-
Lim
+ 1
-
-
t(t 1)
+
t
-
>
0
6
n
(imt
+
-
x0
+
I
(t 1)
+
=lim
x O
t
=
+
⑧
1
=
11) (8 points) Find limit of f(x) at x = – 3, 0, 2, 4.
-
f(x)
Lim
X
-
x
-
=
1:mf(x) 0
z
=
x
3-
=>
>
Lim f(x)
>
-
-
0
((x)
(imf(x)
=4
x
x
-
f(x)
-
=
a
=
e
20
0
=
-
32
=>
y+
=
30
Lim
x
-
3
-
-
-
f(x):DNt
Lim
x
x
-
Lim
f(x) 3
x
2t
-
=
>
(imf(x) DNE
=
x
Lim
X
-
34
f(x)
-
32
2
(im
=
-
x
=>
Lim
x
-
32
f(x)
=
-
f(x)
x4+
2
2
=