c. Answers may vary. Sample: The function values increase
more rapidly. 51. 6 53. 3 55a. 4 b. 3 c. y = 4 • 3X
d. §; 324
Lesson 7-7 pp. 460-466
Go t It? 1. about 43,872 subscribers; 1.05m- $4489.01 3a. about 55 kilopascals b. The decimal
equivalent of 100 % is 1.
Lesso n Ch eck 1. 4 2. 15 3. 0.2 4. 0.94 - $32,577.89 6. If b > 1, then it is exponential growth.
If 0 < b < 1, then it is exponential decay. 7. The value of
n = 1 so the formula becomes A = P(1 + r)f. - The student did not convert 3.5% to a decimal;
A = 500 (l + ° T p j (4‘2)= 500(1.00875)8 = 536.09.
Ex e r c i se s 9. 14, 2 11. 25,600, 1.01 13a. 15,000
b. 0.04, 1.04 c. 1.04 d. 15,000, 1.04, x e. about
39,988 15. $5352.90 17. $634.87 19. $5229.70 - $1277.07 23. 5, 0w.5 25. 100, | 27. about
33,236 29. exponential decay 31. exponential
decay 33. No; the value of the car is about $5243. - Answers may vary. Sample: y = - 4 • 1.05x; this is an
exponential function, but it models neither exponential
growth nor decay because a < 0. 37. neither
39a. P = 400(1.05)n, where n is the number of years
and P is the profit, b. $5031.16 41a. $220 b. $3.96
c. $223.96 d. $193.96 e. 9 m onths f. $18.07
Lesson 7-8 pp. 4 6 7 -4 7 2
Go t I t? 1a. geometric b. arithmetic c. geometric
d. neither geometric nor arithmetic 2 a. an = ar)_ 1 + 2 ,
a, = 2;a„ = 2 + (n-1X 2)
b. an ar (l),a1=40;an = 4 0 .(l)n 1
3a. an = an_i - 6, ai = 14;an =
14 • 6n_1; a8 = 3,919,104 b. an = an • 1, a , =
648; an = 648 • (?)n_1; a8 « 5.06 - f(x) = 2 • 3X_1;
Lesso n Ch eck 1. yes; 3 2. yes; | 3. no
4. a n = 5 • 4n“ 1; a n = an_i • 4, a: = 5- an = 4 • (—2)n1; an = an • ( - 2 ) , a! = 4
6. an = 162 • ( § ) " '; an = a n-| • ( | ) , a 1 = 162
7. an = 3 • (2)n~1; an = an_, • (2), a 1 = 3 8. Answers
will vary. Sample answer: This is the explicit formula. The
recursive formula is a-| = 1, an = a n_i * ( - 1 ). 9. Both
arithmetic and geometric sequences can increase or
decrease. Geometric sequences increase or decrease by a
constant ratio. Arithmetic sequences increase or decrease
by a constant difference.
Ex e r c i se s 1 1. not geometric; no constant ratio- geometric; constant ratio of | 15. geometric;
constant ratio of 2 17. y 19. 4 21.-3 - an = 3 • (2)n- ] 25. an = 3 • (-4 )n~1
- an = 686 • (y) 29. a-1 = 1, a n = an_-| • 5
- a\ = 2, an = an_i • (—4)
- a-1 = 192, an = an-1 * (|)
- an = 48 • ( | ) ; an = an_! • a^ = 48
- f{x) = 8 • 2X 1; The graph of the function passes
through the points (1, 8), (2, 16), (3, 32), (4, 64). 39. not
geometric 4 1. geometric; y;^1 an = 98 • I j) ;
a! = 98, an = an• y - geometric; -j, an = 200 • (-y )° \ a-| = 200,
an = an_i • (- y ) 45. arithmetic - arithmetic 49. geometric 51. Check students'
answers. 53. Both sequences triple for each following
term. However, the first sequence starts at 5, while the
second starts at 10. 55. G 57. 1 - an = 0 + 9n; a^ = 0, an = an_i + 9
- an = 5 + - 2 n ; a! = 0, an = an_-| + (-2)
- an = - 7 + 4n; a-| = - 7 , an = an_-| + 4
- x = -8 63. y = —2 64. a = ^ 65 .7 5 %
increase 66. 37.5 67. 2 x + 5y 68. 4a + 2b
- 4 c + 5d
Chapter Review pp. 474-478- geometric sequence 2. growth factor 3. decay factor
- exponential growth 5. exponential decay 6. 1
7- i 8. ^ 9. 10. 9 11. ^ 12. 1 13. 45 14. f - -yy 16. No; - 3 should be raised to the fourth
power instead of multiplying it by 4. 17. 32 • 38 = 310 - a 6 • a 2 = a 8 19. x2y5 • x3)/6 = x5y 1 1
20. (^11 32) • a 2 = a 21. xs • X 2 4 3 n = xi 2 22. m*m3 1 • m^m =1 1
min 23. 2d5 24.x7 25. -xV 2 26. sit 27. pfgl
- 6 mn3 29. 7.8 X 103 pores 30. 3 31. -5 32. 2
- (xf)2 = x 2 34. (aj)j = al 35. (2x2y l)2 = 4x4^
898