Unit 2
Answer Key
1
Unit 2 Answers
BB-1.
b) 264 c) after 32 months d) t(n) = 12n + 120
e) n = 31.67; 500 is not a multiple of 12.
BB-2.
a) adding 3
BB-3.
a) 10, 12, 14; add 2; yes
b) 16, 32, 64; multiply by 2; yes
c) -1, -3, -5; subtract 2; yes
d) 16, 25, 36; add next odd or next square; no
e) 8,9.5,11; add 1.5; yes
f) 8, 13, 21; add previous 2 terms; no
1 ; divide by 3; yes
g) 13 , 19 , 27
h) 5, 2.5, 1.25; divide by 2; yes
i) 17, 27, 39; add next even number; no
j) 8, 11, 14; add 3; yes
k) 24, 48, 96; multiply by 2; yes
l) 125, 216, 343; cubes; no
BB-4.
c) 14
x
BB-5.
27a6b3
BB-6.
a)
b) -3, 6, -12, 24, -48
c)3, 9, 81, 6561, ...
d) x6 !
8
8
4
8
b) By doubling it.
c) 1, 2, 4, 8, 16, 32, 64,…
4
b) 351 c) 3 ⋅74
BB-7.
a) 52 = 25
d) 6104
BB-8.
a) y = -2x + 7
BB-9.
a) add 1, add 3, add 4 b) 25, 75, 98
c) t(n) = n; s(n) = 3n; p(n) = 4n - 2
BB-10.
a) 14
BB-11.
Find a common denominator (36), convert each fraction to 36ths,
1
subtract; - 36
b) 34
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v. 5.0
Unit 2
Answer Key
2
BB-13.
a) (a), (e), and maybe (c)
c) y-intercept
BB-15.
Because subtracting 2 is the same as adding -2
BB-16.
Multiply by 12 ; (g): multiply by 13
BB-17.
b) (3, 1)
BB-18.
a) (4, 8, 4 3 ), (5, 10, 5 3 ) b) The long leg is 3 times n, and the hypotenuse
is two times n.
BB-19.
no, mAB = - 15 ; mBC = - 13 ; mAC = - 14
BB-21.
0.5
BB-22.
11
a) 12
BB-23.
No. Yes, (d) and (i) are similar; in both cases each stair step is 2 greater than the
previous one.
BB-24.
b) The stairs are equally spaced and can be found by adding the same number
each time.
d) The stairs are spaced in increments that increase by
multiplying by the same number.
e) The quadratic sequences have stair-cases which form an arithmetic sequence.
The geometric sequences have stair-cases which are also geometric.
f) This stair-case turns out to be almost the same as the sequence itself.
BB-25.
a) t(3) = 15, t(4) = 19, t(5) = 23
c) t(n) = 4n + 3
BB-26.
a) 25
b) 43 d) t(n) = 3n + 1 e) the y-intercept
f) the common difference or generator
BB-27.
m = 4, b = -5
BB-29.
y = -3x + 9
BB-30.
parabolas, with y = 2x2 rising most rapidly and y =
BB-31.
Odd numbers; 93; 2n + 1
BB-32.
This is a scalene triangle, because the sides have lengths 29 , 17 , and 20 .
c) 2x3x+ 3
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d)
b) (b), (k), and maybe (h)
2x + 3y
xy
b) t(100) = 403
1 2
x most slowly.
2
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Unit 2
Answer Key
3
BB-34.
a) 6, 6 3
b) 6, 6 2
BB-35.
a) 8m5
BB-36.
a) 19, 22, 25 b) 7; add 3
c) It is the difference between any 2 consecutive terms.
d) 4
e) t(n) = 3n + 7
f) Slope is 3.
BB-37.
No--7.67 is not in the domain of this function.
BB-38.
Arithmetic
BB-39.
a) t(n) = 3n + 5
d) t(n) = 1.5n + 7
BB-40.
e) t(n) = dn + a or t(n) = a + dn
BB-41.
-3 = 5m + b and 360 - 45m + b; t(0) = -43; d = 8
BB-43.
Provide information to include the slope is the common difference, the yintercept is the initial value.
BB-44.
a) yes, 90th term
b) no c) yes, 152nd term d) no
e) no, -64 = n is not in the domain
BB-45.
When solving for n, you will find a value for n that is not a positive integer
value.
BB-46.
b) 248
BB-47.
10 = 15m + b and 106 = 63m + b; m = 2, b = -20, so t(n) = 2n - 20
BB-48.
7
a) 20
BB-49.
(-2, 0), (-4, 0), (0, 8); x = -3
BB-50.
Terry is correct because x is the same as 1x.
BB-51.
a) y = -3x + 7 b) y = -x - 25
BB-52.
a) 2xy2
c) - 25
3y
b) t(n) = 6n + 3
c) t(n) = -5n + 26
c) t(n) = 14n + 10
d) 50x
y
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b) m3n3
c) 27m3n3
d) 3x3
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Unit 2
Answer Key
4
rebound
BB-53.
Use the ratio of !starting!height . The lacrosse ball rebound is 0.653 and the
handball rebound is 0.635.
BB-54.
a) They’re all about the same.
BB-55.
It is approximately linear. Because when the starting height is 0, the rebound
height is 0. The equation is of the form y = kx,where k is the average rebound
ratio.
BB-56.
The ratio rs will be constant. Measurements all had to be to the bottom of the
rebounding ball.
a) The slope is rs .
b) A ball dropped from 0 cm rebounds 0 cm.
BB-57.
a) Doubling the input doubles the output. Multiplying the input by any number
multiplies the output by the same number.
b) No, the pattern from (a) does not apply.
BB-58.
a) 60/(rebound ratio)
b) 200 m. times the rebound ratio
c) 200 m. times (rebound ratio)2; 200 m. times (rebound ratio)3
BB-59.
a) It is geometric; multiply by 12
c) No, the sequence approaches zero.
Half of a positive number is still positive.
BB-60.
a) add 4, t(n) = 4n + 2; subtract 12, t(n) = -12n + 24;
add 4, t(n) = 4n + 1 b) Yes. 18, 54, 162, 648; multiply by 3. 6, 3, 1.5, 0.75;
multiply by 12 . 25, 125, 625, 3125; multiply by 5
c) Answers will vary.
BB-61.
a) 5
BB-63.
b) y = -1 c) x = 0
BB-65.
(g) and (h)
BB-67.
a) 7m
12
BB-68.
a) 94 years
b) From 1966 to 1999, 429 marbles were added. 429
marbles/33years = 13 marbles/yr. c) 17 e) 59 years
BB-69.
domain: reals
a) y ≥ -1
BB-70.
b) 0.8z
c) 1.002x
b) 47p ≈ 1.80
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b) 12
8y
c) mx
b) y ≤ 1
d) 25
c) y ≤ 0
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Unit 2
Answer Key
BB-71.
a) arith.; t(n) = 3n + 1
d) arith.; 7; t(n) = 7n + 5
f) geom., r = 4
BB-72.
16 p + 4 p = 2
b) 36 p -36
p
3
BB-73.
a) geometric, multiply by 2 c) 3
e) 3(2)6 f) 3(2)100
g) 3(2)n
BB-74.
a) 8000 12
c) 8000 12
()
()
6
n
= 125 liters
5
b) neither
c) geom., r = 2
e) arith.; 1; t(n) = x + n
d) yes, using exponents.
()
b) 8000 12
12
= 1.95 liters
liters
BB-75.
100(1.3)4 = 286 cases a) 100(1.30)7= 627 cases
b) 100(1.30)n
BB-76.
a) 10(r)12
b) Answers will vary.
n
c) h(n) = 10(r) , where r is the rebound ratio.
BB-77.
a) Rebound rate is 0.555, so h(n) = 10(0.555)1 = 5.55 feet.
b) h(n) = 10(0.555)10 = 0.028 ft
c) h(n) = 10(0.555)n ft.
BB-78.
Graph consists of three parabolas: one standard, and two opening downward:
one appears "fatter' and one appears "skinnier" than standard. Negative
coefficent causes parabolas to open downward, without changing vertex.
BB-79.
A convenient number, $100, for the initial cost, is a popular strategy. The
surprising answer is that both situations are the same, with a final amount of $84.
BB-80.
a) 0.05x
BB-81.
b) -5, -5, -5, -5, -5
e) whole numbers
BB-82.
a) -3, 1, 5, 9
b) Arithmetic; yes, the terms can be generated knowing the
common difference and the initial value.
c) Yes, it is term 81; let 4n - 3 = 321 and solve for n.
BB-83.
b) 10100 c) n(n + 1)
BB-84.
a) i: 80 ii: 70 b) i: 56 ii: 56
e) 56% - It is the same as (b).
© 2000 CPM Educational Program
b) x + .05x = 1.05x
d) 1.03; 1.0825; 1.0208
1 , 1 , 1 , 1 , 1 d) 1, -2, 4, -8, 16
c) 16
8 4 2
f) the result or sequence values
c) 80%
d) 70%
v. 5.0
Unit 2
Answer Key
6
BB-85.
a) 1.05x b) 0.88x
c) 1.0825x d) 0.775x
BB-86.
a) 1250(1.27)4 = 3252
b) 1250(1.27)n
c) 8000 = 1250(1.27)n, n ≈ 8 weeks
BB-87.
In 14 days they will earn close to the same amount Plan A:
c(n) = 11.50n; Plan B: c(n) = 0.01(2)n
BB-88.
a) 14 increases, so $735 - $280 = $455. b) $1360 = $20n + $100, so 63 guessed
incorrectly.
BB-89.
b) 397 = 7n + 5, n = 56
BB-90.
a) 0.20x
b) x - .20x = 0.80x
BB-91.
a) 0.97
b) 0.75
BB-92.
The two calculations are: 0.80(1.05x) or 1.05(0.80x).
Both = 0.84x.
BB-94.
C(0, 16); A(-30.1, 0); AB = 30.1, so the area is 240.8 sq. units; perimeter is 80.2
units.
BB-95.
a) B: 4s + 3b = 4.36; R: 8s + b = $3.32
b) The soup costs $0.28 and the bread costs $1.08
BB-96.
a) 9x2
BB-98.
Dad + 18n = 1582; 12n = 504; or Dad + 30n = 2086; n = $42 saved and/or paid
per week, Dad = $826
BB-99.
a) 3, 7.5, 12, 16.5, 21 . . . b) 3, 6, 12, 24, 48 . . .
c) 0.925
2
d) 3x
BB-100. y = 3x + 10
a) 24 b) 64
c) That a 3:1 ratio was used to adjust the points.
BB-101. t(1) = 5; t(3) = 10; if m is the multiplier,
then t(1) = 5m and t(2) = 5m2= 10, so m2= 2.
BB-102. a) 3y + 5 = 14, y = 3
b) 3y + 5 = 32, y = 9
BB-103. a) 0, -50; 75, 125
b) 25, 12.5; 50 2 , 100 2
c) t(n) = 100 - 50n, f(x) = 50 + 25x; t(n) = 100(0.5)n,
x
f(x) = 50 ( 2 )
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v. 5.0
Unit 2
Answer Key
7
BB-104. Both have the same shape as y = x2, one is shifted up 3 units, the other is shifted
left 3 units.
BB-105. b) -1 ≤ x ≤ 1; -1 ≤ y ≤ 2
d) -2 ≤ x ≤ 1; -2 ≤ y ≤ 2
BB-106. b) 5x 2+ 3
x
BB-107. a)
16x8y4
c) -2 < x ≤ 2; -2 ≤ y < 2
c) 7
y3
b) - 12
7
c) 16x
3y
d) 125x5y3
BB-108. b) 38 for exactly 2 tails; 12 including the outcome "three tails."
BB-113. Fifth year means n = 4, so t(n) = $673,500(1.2)4 = $1,396,569.60
a) $875,900 = x(1.15)3, x = $575,918.47
b) s(n) = 673,500(1.20)(n-1); s(n) = 575,918(1.15)(n-1)
c) $5,011,917; $3,883,058
BB-114. a) y = 0.365x b) y = 0.3x + 0.39 c) $7.59; discuss the fact that they generally
charge less per can for larger quantities.
d) $0.365, $0.3325, $0.31625
e) No, zero cans would cost $0.39, the slope represents the approximate cost
per can.
BB-115. a) -350 = -60n + 10, n= 6, yes
b) -350 = 10(-5)n; for n = 2, 250; for n = 3, -1250. No.
m + 3mt
t
2
BB-116. a) 6x
b)
c)
3y - x
y2
BB-117. a) 120 (Rectangular numbers, BB-83, is helpful.)
n(n +1)
c)
2
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d)
6x 2 + 4x - xy - 3y
2xy
b) 20100
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