Question 1

Find the exact solution, using common logarithms, and an approximation of the solution of the equation to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

One method of estimating the thickness of the ozone layer is to use the formula   , where I o  is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, and k is the absorption constant of ozone for that wavelength. Suppose a wavelength of   cm with k = 0.36 ,   is measured as 1.12. Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.

Accepted Answer

A) x = 0.31 cm 
B) x = 3.43 cm 
C) x = 0.04 cm 
D) x = 3.11 cm 
E) x = 0.18 cm 
A) x = 0.31 cm 
B) x = 3.43 cm 
C) x = 0.04 cm 
D) x = 3.11 cm 
E) x = 0.18 cm

Question 3

Ventilation is an effective way to improve indoor air quality. In nonsmoking restaurants, air circulation requirements (in   ) are given by the function   , where x is the number of people in the dining area. Find   . Use   to determine the maximum number of people that should be in a restaurant having a ventilation capability of 2,350   .

Accepted Answer

A) 55 
B) 56 
C) 62 
D) 68 
E) 61 
A) 55 
B) 56 
C) 62 
D) 68 
E) 61

Question 4

Find the solution of the equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V 1  to V 2 , and the decibel increase is given by   Find the decibel increase if the voltage changes from 2.2 volts to 3.5 volts.

Accepted Answer

A) db = 9.3 
B) db = 2.9 
C) db = 6.3 
D) db = 7.8 
E) db = 4.0 
A) db = 9.3 
B) db = 2.9 
C) db = 6.3 
D) db = 7.8 
E) db = 4.0

Question 6

Find the exact solution, using common logarithms, and an approximation of the solution of the equation to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find the solution of the equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Express in terms of logarithms of x, y, or z.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

If $900 is deposited in a savings account that pays interest at a rate of   % per year compounded continuously, find the balance after 7 years.

Accepted Answer

A) $1,418.56 
B) $581.08 
C) $1,369.77 
D) $1,393.95 
E) $3,484.87 
A) $1,418.56 
B) $581.08 
C) $1,369.77 
D) $1,393.95 
E) $3,484.87

Question 10

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V 1  to V 2 , and the decibel increase is given by   Find the decibel increase if the voltage changes from 1.8 volts to 4.1 volts.

Accepted Answer

A) db = 10.2 
B) db = 5.3 
C) db = 14.8 
D) db = 8.7 
E) db = 6.4 
A) db = 10.2 
B) db = 5.3 
C) db = 14.8 
D) db = 8.7 
E) db = 6.4

Question 11

If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula y = y o e -0.3937t  , where t is the time in years and y o  is the pollutant level at which further pollution ceased. How many years would it take to clear 59% of the pollutants?

Accepted Answer

A) t = 0.58 years 
B) t = 1.34 years 
C) t = 2.02 years 
D) t = 0.98 years 
E) t = 2.26 years 
A) t = 0.58 years 
B) t = 1.34 years 
C) t = 2.02 years 
D) t = 0.98 years 
E) t = 2.26 years

Question 12

Change to logarithmic form.

Accepted Answer

A) log 100 = 3 
B) ln 100 = 2 
C) ln 100 = 3 
D) log 100 = 2 
E) log 2 = 200 
A) log 100 = 3 
B) ln 100 = 2 
C) ln 100 = 3 
D) log 100 = 2 
E) log 2 = 200

Question 13

Determine the range of   for the function without actually finding   . Hint: First find the domain and range of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Use common logarithms to solve for x in terms of y.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Determine the range of   for the function without actually finding   . Hint: First find the domain and range of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Solve the equation.

Accepted Answer

A) 18 
B) 7 
C) 1 
D) 9 
E) 8 
A) 18 
B) 7 
C) 1 
D) 9 
E) 8

Question 17

Write the expression as one logarithm. 9ln ( x ) - 7ln   - 4ln ( xy )

Accepted Answer

A) ln ( x 9  - y 7  - ( xy )  4  ) 
B) ln ( 9x - 7y - 4xy ) 
C) ln ( x 3 y 5  ) 
D) ln ( x 5 y 3  ) 
A) ln ( x 9  - y 7  - ( xy )  4  ) 
B) ln ( 9x - 7y - 4xy ) 
C) ln ( x 3 y 5  ) 
D) ln ( x 5 y 3  )

Question 18

The graph of a one-to-one function f is shown. Find the domain D and range R of the inverse function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut,   , where N o  is the initial size of the cohort. Approximate the percentage of the original number still alive after 9 years.

Accepted Answer

A) 5.5% 
B) 50.4% 
C) 33.1% 
D) 16.5% 
E) 18.0% 
A) 5.5% 
B) 50.4% 
C) 33.1% 
D) 16.5% 
E) 18.0%

Question 20

Sketch the graph of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find the exact solution, using common logarithms, and an approximation of the solution of the equation to two decimal places.

Find the solution of the equation.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V₁ to V₂, and the decibel increase is given by Find the decibel increase if the voltage changes from 2.2 volts to 3.5 volts.

Find the exact solution, using common logarithms, and an approximation of the solution of the equation to two decimal places.

Find the solution of the equation.

Express in terms of logarithms of x, y, or z.

If $900 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 7 years.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V₁ to V₂, and the decibel increase is given by Find the decibel increase if the voltage changes from 1.8 volts to 4.1 volts.

Change to logarithmic form.

Determine the range of for the function without actually finding . Hint: First find the domain and range of

Use common logarithms to solve for x in terms of y.

Determine the range of for the function without actually finding . Hint: First find the domain and range of

Solve the equation.

Write the expression as one logarithm. 9ln ( x ) - 7ln - 4ln ( xy )

The graph of a one-to-one function f is shown. Find the domain D and range R of the inverse function .

Sketch the graph of

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

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Exam 5: Inverse, Exponential, and Logarithmic Functions

Find the exact solution, using common logarithms, and an approximation of the solution of the equation to two decimal places.

Find the solution of the equation.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V 1 to V 2 , and the decibel increase is given by Find the decibel increase if the voltage changes from 2.2 volts to 3.5 volts.

Find the exact solution, using common logarithms, and an approximation of the solution of the equation to two decimal places.

Find the solution of the equation.

Express in terms of logarithms of x, y, or z.

If $900 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 7 years.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V 1 to V 2 , and the decibel increase is given by Find the decibel increase if the voltage changes from 1.8 volts to 4.1 volts.

Change to logarithmic form.

Determine the range of for the function without actually finding . Hint: First find the domain and range of

Use common logarithms to solve for x in terms of y.

Determine the range of for the function without actually finding . Hint: First find the domain and range of

Solve the equation.

Write the expression as one logarithm. 9ln ( x ) - 7ln - 4ln ( xy )

The graph of a one-to-one function f is shown. Find the domain D and range R of the inverse function .

Sketch the graph of

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V₁ to V₂, and the decibel increase is given by Find the decibel increase if the voltage changes from 2.2 volts to 3.5 volts.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V₁ to V₂, and the decibel increase is given by Find the decibel increase if the voltage changes from 1.8 volts to 4.1 volts.