IMSA
1.
MI-3
Problem Set 3 DUE: Tues., Feb. 7
Spring '12
If log x  5  p and log x  3  t . Determine each of the following in terms of p and/or r..
 25 
log x  
 27 
a.
2.
b. log27  25
A bag contains 8 orange balls, 6 green balls, and 4 blue balls.
a.
If a ball is drawn at random, what is the probability it is blue?
b.
c.
If two balls are drawn, what is the probability that the first is orange and the second is green?
If two balls are drawn, what is the probability that neither is orange?
3.
At age 22, when he had just $4000, Quincy Q. Quarp discovered a way to double savings every
three years. At age 39, he realized that he had already saved half as many years as would be
necessary to reach his retirement goal. At what age did he have half as much money as he wanted
for retirement?
4.
At a small party, each person greets each other person by shaking hands.
How many handshakes take place if the numbers of people is:
a. 3
b. 5
c. 108
d.
k
5
5.
Find the value of k if :
 ln(3 j  1)  ln(k )
j 1
NC
6.
Solve for x :
a.
 log2 ( x) 2  3  log2 ( x)  18  0
b.
log4 (9)   log9 ( x)  =
4
nt
7.
 r
Remember the compound interest formula: A  P  1   . Suppose that $1 is an initial
 n
investment at 100% interest for 1 year.
a. Make a table for n, number of compounding periods, and A(n) as shown on the answer sheet.
b. Plot the graph of A(n) vs. n with appropriate labels. What can you say about the values of A(n) as
n  ?
8.
If a group of people is asked to memorize a list of nonsense words, then the percent of those who
remember all the words after t hours can be approximated by the logarithmic function
f (t )  1  k ln(t  1) , where k is a constant that depends on the length of the list of words and other
factors.
a. Determine the value of k based on the observation that after 5 hours only 20% of the members
of a group can remember all the words.
b. Using this value of k, determine what percent remember all the words after 1 hour.
c. At what time will no one in the group be able to remember all the words?
PS 3.1
Rev. S12
IMSA
9.
MI-3
Problem Set 3
DUE: Tues., Feb. 7
Spring '12
There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four
representatives to the State Conference.
a) How many different ways are there to select a group of four students to attend the conference?
b) If the members of the club decide to send two juniors and two seniors, how many different
groupings are possible?
10.
Determine the domain for each function :
a.
11.

f ( x)  ln x2  7 x  10

g ( x)  ln  x  2  ln  x  9 
b.
The radii of two circles are ln(2) and ln(8) respectively. Find the ratio of:
a. the circumference of the large circle to that of the small circle.
b. the area of the large circle to that of the small circle.
NC 12.
Solve for x over the real numbers.
a.
13.
x 2  12 x  32  0
 log 2 x 
b.
If  log3 4  log4 5  log5 6  . . . (log3031) (log3132) =
2
 12  log 2 x   32  0
a
, determine the value of (a + b).
b  log 2 (3)
D
14.
DE = log (32), BC = log (8), and AC = 12.
B
3
3
Find AE.
A
15.
C
E
Point P  a, b  is on the graph of
32
and a  b  17 . Find the distance OP
x
from the point P to the origin.
y
PS 3.2
Rev. S12
IMSA
MI-3
16. Show that log a
17.

Problem Set 3

x  x  1  log a

DUE: Tues., Feb. 7
Spring '12

x  x 1  0
DECIBEL (dB) SCALE
Intensity of sound is described using a logarithmic scale. The scale, which was named after Alexander
Graham Bell, is called the decibel scale. The scale relates the intensity (measured in watts/m2) to decibels.
2
Loudness level
(decibels)
Intensity (watts/m )
0
10
barely audible
normal breathing
10
-12
10
-11
20
rustling leaves
10
-10
30
soft whisper
10
-9
40
quiet library
10
-8
50
quiet radio
10
-7
60
normal conversation
10
-6
70
busy street traffic
10
-5
80
factory
10
-4
90
Niagara Falls
10
-3
100
siren (at 30 m)
10
-2
110
loud thunder
10
-1
120
amplified rock music (3 m away)
10
0
130
pain level
10
1
140
jet plane (30 m away)
10
2
160
rupture of eardrum
10
4
a. How many times more intense is a normal conversation than a soft whisper?
b. The intensity of a jet plane at 600 m is 30 dB more than that of a pneumatic drill at 15 m.
How many times more intense is the sound of the jet?
PS 3.3
Rev. S12