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Extra Practice
Chapter 7- Algebra
Lessons 7-1 to 7-5
Simplify each expression. Use only positive exponents.
1. (2t)-6
2. 5m5m-8
3. (4.5)4(4.5)-2
4. (m7t-5)2
5. (x2n4)(n-8)
6. (w-2j-4)-3( j7j3)
7. (t 6)3(m)2
8. (3n4)2
w7
w-6
10.
1
a -4
11.
13.
a2 b-7 c4
a5b3 c-2
(2t )
14.
æ c5 c-3 ö
16. ç -4 ÷
è c ø
-2
9.
12.
5 3
6
t -4
æ a6 ö
15. ç 7 ÷
èa ø
4t 8t -1
æ 4 x3 ö
17. ç -2 ÷
è 8x ø
r5
g -3
0
-3
æ y-3 ö
18. ç 3 ÷
è y ø
2
Evaluate each expression for m = 2, t = 3, w = 4, and z = 0.
19. tm
20. t-m
21. (w · t)m
22. wm · tm
23. (wz)m
24. wmwz
25. z-t(mt)z
26. w-ttt
æ tw ö
27. ç
t÷
èm ø
z
Write each number in scientific notation.
28. 34,000,000
29. 0.00063
30. 1500
Write each number in standard notation.
31. 8.05 × 106
32. 3.2 × 10-7
33. 9.0 × 108
34. The speed of sound is approximately 1.2 × 103 km/h. How long does it take
for sound to travel 7.2 × 102 km? Write your answer in minutes.
Lesson 7-6 Evaluate each function over the domain {1, 0, 1, 2}. As the values of the
domain increase, do the values of the function increase or decrease?
x
35. y = 3x
37. y = 1.5x
æ3ö
36. y = ç ÷
è4ø
Write and solve an exponential equation to answer each question.
38. Suppose an investment of $5,000 doubles every 12 years. How much is the investment worth
after 36 years? After 48 years?
39. Suppose 15 animals are taken to an island, and then their population triples every 8 months.
How many animals will there be in 4 years?
40. The population of a city this year is 34,500. The population is expected to grow by 3% each
year. What will be the population of the city in 12 years? When will the population be over
100,000?
Lesson 7-7 Write an exponential function to model each situation. Find each amount after
the specified time.
41. $200 principal, 4% growth compounded semi-annually for 5 years
42. $3000 investment, 8% loss each year for 3 years.
43. Given the equation y = .2•4x, evaluate for x =10. What does the 10 represent?
Sketch the graphs WITHOUT using your calculator. Label your axes.
44. y = 3 • 2x
45.
y = 30 • (½)x
Lesson 7-8a Using your calculator, find a regression line for the following data. Round to
the nearest tenth.
46. (1, 115) (2, 527) (4, 10,660) (5, 47,980) (6, 215,898)
Lesson 7-9a
47. For the following Sequence, 7, 28, 112, 448, 1792, … Write a both a recursive equation and
an explicit equation using subscripts. What is A7? A0?
48. If An = An-1 x ½ and A2 = 20, what is A5?