Prentice Hall Algebra 2

Chapter 7 Exponential and Logarithmic Functions > 7 Cumulative Test Prep

7 Cumulative Test Prep

Tips For Success

Some problems ask you to find lengths of arcs or areas of sectors. Read the question below. Then follow the tips to answer the sample question.

Tip 1

Draw a diagram

A circle has a radius of 6 centimeters. Two line segments extend from the center of the circle to the circle edge with an area of 60 degrees between them.

Tip 2

Find f ( x ) first . f ( x ) = π r 2 f open x close , first , . f open x close equals , pi r squared

= π · 6 2 = 36 π equals pi middle dot , 6 squared , equals 36 pi

Let f ( x ) = π x 2 f open x close equals , pi x squared represent the area of a circle with radius x. Let g ( x ) = 60 x 360 cap let , g open x close equals . fraction 60 x , over 360 end fraction represent the area of a 60 degrees sector of a circle with area x. A circle with radius 6 centimeters has a sector measuring 60 degrees . What is the area of this sector open g composition f close open x close question mark

6 pi , cm squared
12 pi cm squared
24 pi cm squared
36 pi cm squared

Think It Through

g ( x ) = 60 x 360 ( g ο f ) ( x ) = 60 ( 36 π ) 360 = 36 π 6 = 6 π table with 4 rows and 2 columns , row1 column 1 , g open x close , column 2 equals . fraction 60 x , over 360 end fraction , row2 column 1 , open g omicron f close open x close , column 2 equals . fraction 60 open 36 pi close , over 360 end fraction , row3 column 1 , , column 2 equals , fraction 36 pi , over 6 end fraction , row4 column 1 , , column 2 equals 6 pi , end table

The correct answer is A.

Vocabulary Builder

As you solve problems, you must understand the meanings of mathematical terms. Match each term with its mathematical meaning.

growth factor
asymptote
logarithmic function
exponential equation

the inverse of an exponential function
a line that a graph approaches as x or y increases in absolute value
the value of b in y = a b x , y equals , eh b to the x , comma when b greater than 1
an equation of the form b c x = a , b c to the x , equals eh comma where the exponent includes a variable

Multiple Choice

Read each question. Then write the letter of the correct answer on your page.

The population of a town is modeled by the equation P = 16 , 581 e 0.02 t p equals 16 comma . 581 e super 0.02 , t end super where P represents the population t years after 2000. According to the model, what will the population of the town be in 2020?
1. 16,916
2. 17,258
3. 20,252
4. 24,736
If i = − 1 , i equals , square root of negative 1 end root . comma then which expression is equal to 9 i ( 13 i ) ? 9 to the i , open , 13 to the i , close question mark
1. negative 117
2. 117 to the i
3. 117
4. negative , 117 to the i
Which expression is equivalent to log 5 32 ? log base 5 , 32 question mark
1. log 5 + log 32
2. log 5 minus log , 32
3. (log 5)(log 32)
4. log 32 log 5 fraction log , 32 , over log 5 end fraction

End ofPage 492

7 Cumulative Test Prep

Tips For Success

Tip 1

Tip 2

Think It Through

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