Advanced Algebra
Chapter 7 Review
Name ______________________________
Useful Formulas. On the test you will not be given the formulas for geometric sequences, but you will be
given the compound interest formula.
Compound Interest:
Geometric Sequences:
nt
Recursive Formula
Explicit Formula
æ rö
A = Pç1+ ÷
ì g1
è nø
í
gn = g1 (r)n-1, for n ³1
Where r is the interest rate (as a
î gn = rgn-1, for n ³ 2
decimal) compounded n times per
year:
where n = the term # and
gn-1 = the previous term
r = the common ratio (multiplier)
g1= first term and gn = nth term
SECTION I:
Calculators may (must) be used for this section.
Round all values of money to the nearest hundredth.
1. Annie puts $450 into a savings account that pays 2.8% interest, compounded quarterly. Assuming
that she makes no other deposits or withdrawals, how much money will she have in the account after
3 years?
P = ___________
r = ___________
n = ___________
t = ___________
2.
A = ___________
Dan invests $2500 in a savings account that earns an interest rate of 3.3% compounded
monthly. How much will he have in the account in 4 years, assuming he makes no deposits or
withdrawals in that time period?
P = ___________
r = ___________
n = ___________
t = ___________
3.
A = ___________
A bond paying 6.8% compounded daily for 10 years has matured. Lulu received $10,000 after it
matured. How much did she pay for the bond 10 years ago?
P = ___________
r = ___________
n = ___________
t = ___________
A = ___________
4.
William now has $4000 in a savings account that has been earning interest at a rate of 3.8%
compounded quarterly. How much was in the account four years ago, assuming that he made no
deposits or withdrawals in that time period?
5.
Martha puts $875 into a savings account that pays 3.6% interest, compounded monthly. Assuming
that she makes no other deposits or withdrawals, how much money will she have in this account
after 2 years?
6. The average pulse rate P beats per minute for persons t cm tall is approximated by the formula
-
1
2
P = 940t . Find the average pulse rate for people 160 cm tall. (Round to the nearest tenth).
7.
In 1992, the population of the United States was approximately 255 million. In that year,
Americans consumed about 1.44 ´1011 pounds of dairy products. Find the average amount of dairy
consumption per person in 1992.
2
8. The formula d =1.82r 3 gives an excellent approximation of a planet’s average distance from the sun
in millions of miles, when the number of Earth days r that it takes for the planet to make one
revolution around the sun is know. Mars revolves around the sun once every 687 days. What is the
average distance of Mars from the sun?
3
9. Estimate (0.1587)–5 to the nearest thousandth.
10. Solve for d. d
–
5
2
= 53
Consider the geometric sequence 4, 6, 9, 13.5, ….
11. Give the constant ratio of the sequence.
12. Name the next 2 numbers in the sequence.
13. Find a recursive formula for the sequence.
14. Find an explicit formula for the nth term.
Given these equations, find the first 4 terms of each sequence. Also, identify whether the formula is
written in recursive or explicit form.
ì g1 = 32
15. gn = -3× 2 n-1
ï
16. í
1
ïî gn = - gn-1 for n ≥ 2
2
______, ______, ______, ______, . . .
Form (circle one):
explicit
recursive
______, ______, ______, ______, . . .
Form (circle one):
explicit
17. a. Write an equation for this nth power function.
b. Give the coordinates of four other points that lie on the graph of this function.
recursive
PART II: NO CALCULATORS. You may use your multiplication and power charts.
In 1-8, write as a whole number or simple fraction.
1. 8–2
æ 3ö
3. ç ÷
è 5ø
5.
4
2. 343 3
–2
2
4. 243 5
æ 81 ö
çè
÷
625 ø
-
æ 81 ö
7. ç
÷
è 625 ø
–
3
4
1
4
6. (16 -8 )0
8.
6 × 2 –3
2 × 3-2
9. Consider the function f with equation f (x) = x n , where n is an odd or an even positive number.
if n is odd
if n is even
a. The domain
b. The range
c. In what quadrants is
the graph of f ?
d. Describe the type of
symmetry
10. Which of these values are 5th roots of 32? Justify your answers.
a. 2
b. 2i
c. -2i
In 11 and 14 simplify with ONLY positive exponents in your answer.
2x -3 y
12. (4a-3b)× (2a 2 b)-2
11.
3x 2 y -5
13.
(2x 2 y)3 × (2x 3 y5 )2
Solve.
15. 34 = (3m)2
2
5
17. x = 9
19. g
21. q
-
4
3
-
2
5
56m –3n –1
7m –5 n 4
16. 43 = (2y)5
18. b
= 625
=
14.
9
4
3
–5
2
3
= 216
20. x =
4
9
22. 4t 5 – 9 = 963
(can use your calc to divide)
23.
Matching. Which graph could represent the function with equation:
a. y = x10 __________
i)
y
b. y = x17 __________
ii)
iii)
y
x
x
24. Write in scientific notation:
a. 21,000,000
b. 0.0000076
d. (11×10-5 )3
e. .0000556
f. (6 x 104)2
( 4 ×10 ) (3×10 )
8
y
x
c. (5×103 )2
g.
c. y = -x17 __________
-2
h.
9 ×10 22
3×1018
PART I Answers
æ .028 ö
1. A = 450 ç1+
÷ » $489.29
è
4 ø
æ .033 ö
2. A = 2500 ç1+
÷
è
12 ø
æ .068 ö
10, 000 = P ç1+
÷
3.
è 365 ø
P » $5066.49
æ .038 ö
4, 000 = P ç1+
÷
4.
è
4 ø
P » $3438.42
3×4
10×365
4×12
» $2852.25
4×4
æ .036 ö
5. A = 875ç1+
6. 74.3 beats per minute
÷ » $940.22
è
12 ø
1.44 ´1011
7.
= 0.005647´10 5 » 564.70 pounds of dairy per person in 1992. (Wow!)
6
255´10
12×2
2
3
8. d =1.82(687) » 141.7 million miles.
9. 0.331
10. 0.204
ì g1 = 4
11. 1.5
12. 20.25, 30.375
13. í
14. gn = 4 ×1.5n-1
î gn =1.5gn-1 for n ≥ 1
15. -3, -6, -12, -24, . . explicit
16. 32, -16, 8, -4, 2, . . . recursive
7
17. a. f (x) = x
b. (0,0), (4, 16384), (1, 1), (-1, -1), (2, 128), (-2, -128), etc.
PART II Answers
1.
2. 2401
1
64
3.
4. 9
25
9
5.
6. 1
125
27
7.
5
3
8.
27
8
9.
If n is odd:
a. D = all real numbers
If n is even:
a. D = all real numbers
b. R = all real numbers
c. I and III
d. rotational symmetry
b. R = y ≥ 0
c. I and II
d. reflection symmetry
10. a. 2× 2× 2× 2× 2 = 32 (yes)
b.
2i × 2i × 2i × 2i × 2i = 4i2 × 4i2 × 2i = 32i (no)
c. -2i ×-2i ×-2i ×-2i ×-2i = 4i2 × 4i2 ×-2i = -32i (no)
2y 6
11.
3x 5
1
12. 7
ab
13. 32x y
17. x = 243
18. b =
22. t = 3
23. a) i
1
16. y = 2 5
21. x =
32
243
24. a) 2.1 x 107
e) 5.56 x 10-5
b) 7.6 x 10-6
f) 3.6 x 109
8m 2
14. 5
n
12 13
1
1776
19. g =
b) iii
c) 2.5 x 107
g) 1.2 x 107
1
125
15. m = 3
20. x =
c) ii
d) 1.331 x 10-12
h) 3 x 104
8
27