Page 215 - Algebra 1

Example
4
200 Saxon Algebra 1
Application: The Intensity of Sound
The intensity of sound can be measured in watts per square meter. The table below lists intensity levels for some common sounds.
Intensity of Sound
Math Reasoning
Write Which value is greater, 10-2 or 101? Explain.
Watts/Square Meter
Common Sound
103 to 107
Rocket Liftoff
100 to 102
Jet Liftoff
10-2 to 100
Loud Music
10-6 to 10-4
Vacuum Cleaner
10-9 to 10-6
Regular Speech
10-10 to 10-9
Soft Whisper
How many times more intense is the sound of a rocket liftoff at
103 watts per square meter than that of regular speech at 10-7 watts per square meter?
Express the answer in exponential and standard form.
Math Language
1010 is in exponential form. 10,000,000,000 is in standard form.
SOLUTION
_3 10
10-7
= 103-(-7)
= 1010
= 10,000,000,000
Write a ratio to compare the sound intensities.
Quotient Property of Exponents Simplify the exponent.
Simplify.
The sound of a rocket liftoff is 1010 or 10,000,000,000 times more intense than that of regular speech.
Simplify each expression. All variables represent nonzero real numbers.
Lesson Practice
(Ex 1)
a. x b. q4 c. d-8
(Ex3)
f.
i.
(Ex 4)
x9 xy-3z5 _ _
Refer to the table in Example 4. How many times more intense is
the sound of a jet liftoff at 101 watts per square meter than that of a vacuum cleaner at 10-5 watts per square meter? Express the answer in exponential and standard form.
-5 p-8
_ _1
Evaluate each expression for a = 4, b = 6, and c = 3. (Ex 2)
d. a0bc2 e. 4a-2
Simplify each expression. All variables represent nonzero real numbers.
x10 _
x4
g. x-2 h. y2x2z