Intermediate Algebra (11th edition)

34.B. G. Thompson puts $1000 in a retirement account at the end of each quarter of a year
for 15 yr. If the account pays 4% annual interest compounded quarterly, how much will be
in the account at that time?

35.At the end of each quarter, a 50-year-old woman puts $1200 in a retirement account that
pays 5% interest compounded quarterly. When she reaches age 60, she withdraws the en-
tire amount and places it in a mutual fund that pays 6% interest compounded monthly.
From then on, she deposits $300 in the mutual fund at the end of each month. How much
is in the account when she reaches age 65?

36.Derrick Ruffin deposits $10,000 at the end of each year for 12 yr in an account paying 5%
compounded annually. He then puts the total amount on deposit in another account paying
6% compounded semiannually for another 9 yr. Find the final amount on deposit after the
entire 21-yr period.

Find the sum, if it exists, of the terms of each infinite geometric sequence. See Examples 8
and 9.

37. , 38. ,

39. , 40. ,

41. 42.

43. 44.

Solve each application. (Hint: Immediately after reading the problem, determine whether you
need to find a specific term of a sequence or the sum of the terms of a sequence.)

45.When dropped from a certain height, a ball rebounds of the
original height. How high will the ball rebound after the
fourth bounce if it was dropped from a height of 10 ft?

46.A fully wound yo-yo has a string 40 in. long. It is allowed to drop, and on
its first rebound it returns to a height 15 in. lower than its original height.
Assuming that this “rebound ratio” remains constant until the yo-yo
comes to rest, how far does it travel on its third trip up the string?

47.A particular substance decays in such a way that it loses half its weight each day. In how
many days will 256 g of the substance be reduced to 32 g? How much of the substance is
left after 10 days?

48.A tracer dye is injected into a system with an ingestion and an excretion. After 1 hr, of

the dye is left. At the end of the second hour, of the remaining dye is left, and so on. If

one unit of the dye is injected, how much is left after 6 hr?

2

3

2

3

3

5

a

q

i= 1

a-

16

3

ba-

9

8

b

i

a

q

i= 1

12

5

a

5

4

b

i

a

q

i= 1

3

5

a

5

6

b

i

a

q

i= 1

9

8

a-

2

3

b

i

r=-

3

5

r=- a 1 = 8800

1

10

a 1 = 1000

r=

1

5

r= a 1 = 10

1

3

a 1 = 6

A^14 B

SECTION 12.3 Geometric Sequences 699