49.In a certain community, the consumption of electricity has increased about 6% per yr.
(a)If a community uses 1.1 billion units of electricity now, how much will it use 5 yr
from now?
(b)Find the number of years it will take for the consumption to double.
50.Suppose the community in Exercise 49reduces its increase in consumption to 2% per yr.
(a)How much will it use 5 yr from now?
(b)Find the number of years it will take for the consumption to double.
51.A machine depreciates by of its value each year. If it cost $50,000 new, what is its value
after 8 yr?
52.Refer to Exercise 46.Theoretically, how far does the yo-yo travel before coming to rest?
1
4
700 CHAPTER 12 Sequences and Series
EXERCISES 53–58
FOR INDIVIDUAL OR GROUP WORK
In Chapter 1,we learned that any repeating decimal is a rational number; that is, it can
be expressed as a quotient of integers. Thus, the repeating decimal
with an endless string of9s,must be a rational number. Work Exercises 53 –58 in order,
to discover the surprising simplest form of this rational number.
53.Use long division to write a repeating decimal representation for.
54.Use long division to write a repeating decimal representation for.
55.Because , the sum of the decimal representations in Exercises 53 and 54
must also equal 1. Line up the decimals in the usual vertical method for addition,
and obtain the repeating decimal result. The value of this decimal is exactly 1.
56.The repeating decimal can be written as the sum of the terms of a
geometric sequence with and.
Since , this sum can be found from the formula. Use this
formula to support the result you found another way in Exercises 53 – 55.
57.Which one of the following is true, based on your results in Exercises 55 and 56?
A. B. C.
58.Show that 0.49999Á=^12.
0.99999Á6 1 0.99999Á= 1 0.99999ÁL 1
S=
a 1
1 - r
|0.1| 61
0.99999Á=0.9+0.9 1 0.1 2 +0.9 1 0.1 22 +0.9 1 0.1 23 +0.9 1 0.1 24 +0.9 1 0.1 25 +Á
a 1 =0.9 r=0.1
0.99999Á
1
3 +
2
3 =^1
2
3
1
3
0.99999Á,
RELATING CONCEPTS
Multiply. See Section 5.4.
- 1 a-b 23 62. 1 x+y 24
13 x+ 2 y 22 14 x- 3 y 22
PREVIEW EXERCISES
