COLLEGE ALGEBRA
MATH 110
Southwestern   
Adventist University 
 
   Distance Education Lawrence E. Turner, Jr., Ph.D.  


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SAMPLE TEST QUESTIONS

1999

(Barnett, Ziegler, and Byleen)


Chapter 5     Exponential and Logarithmic Functions

5.1     exponential functions

69.     How does the graph of f(x) = 2x relate to the graph of g(x) = (1/2)x?
(5)


70.     What is the value of all exponential functions at x = 0?
(3)


71.     The population of Texas grows at the rate of 3% increase each year. If the population were 16,400,000 in 1985, then what would be the population in 2005?
(5)


72.     An investment grows exponentially in such a way that it doubles in 10 years. If $1000 is invested initially, then what is the amount after 7 years?
(5)


5.2     the exponential function with base e

73.     Simplify:
(5)


74.     Sketch the graph for:
(5)


75.     The spread of a certain epidemic is governed by

where N(t) is the number that have been infected in the population, and t is measured in days.
  1. what is the initial number infected; that is, N(t=0)?
    (5)
  2. what value does N approach as t gets large; that is, what is the horizontal asymptote?
    (5)
  3. sketch the graph of this function for 0 le t le 20 days.    
    (5)


5.3    logarithmic functions

76.     How does the graph of f(x) = 2x relate to the graph of g(x) = log2 x?
(5)


77.     What is the value of all logarithmic functions at x = 1?
(5)


78.     If ex = 3, then what is the value of x?
(5)


79.     If ln x = -1, then what is the value of x?
(5)


80.     Simplify; that is, write as a single log function or simpler:
  1.  
    (5)
  2.  
    (5)

81.     Compute the values of the following. Hint, you do not need a calculator.
  1.  
    (3)
  2.  
    (3)
  3.  
    (3)
  4.  
    (3)
  5.  
    (3)


5.4     common and natural logarithms

82.     Compute the following values to 4 digits to the right of the decimal point:
  1.  
    (3)
  2.  
    (3)
  3.  
    (3)
  4.  
    (3)
  5.  
    (3)
  6.  
    (3)
  7.  
    (3)
  8.  
    (3)
  9.  
    (3)
  10.  
    (3)
  11.  
    (3)
  12.  
    (3)


83.     Tritium, a radioactive isotope of hydrogen, has a half-life of 12.33 years. It is used, when mixed with a phosphorescence substance, to illuminate watch dials, rifle sights, etc. for night use. If 0.1 milligrams is used, how much remains after
  1. 5 years?
    (5)
  2. 20 years?
    (5)

84.     It is determined that a wooden beam taken from the ruins of a house has 30.7% of the amount of C14 as a freshly cut log. The amount of C14 is in equilibrium when the entity is living. When it dies, the amount of C14 decays with a half-life of 5730 years. That is,

where the amount at time t, A(t), is calculated from the initial amount, Ao, and the half-life, H.

How long has it been since the wooden beam was harvested from its tree and incorporated into the structure of the house?
(10)


85.     The atmospheric pressure P, in pounds per square inch, decreases exponentially with altitude h, in miles (5280 ft/mi) above sea level, as given by

  1. What is the air pressure, in pounds per square inch, at the peak of Mt. Everest which is 29035 ft.
    (5)

  2. What is the air pressure, in pounds per square inch, at the Dead Sea which is 1312 feet below sea level?
    (3)

86.     The sound level of a sound is measured in decibels which are defined according to:

where Io = 10-16 watts per square centimeter.
  1. If a whisper has a sound intensity of 5.2x10-14 watts/square centimeter, then what is the sound level of a whisper in decibels?
    (5)

  2. If the noise of rustling leaves has a sound level of 10 db, then what is the sound intensity in watts/square centimeter?
    (5)

87.     The specification for an audio amplifier states that the signal-to-noise ratio is -50 db. This means the sound level of the noise in the system is 50db less than the sound level of the normal music. This difference in sound level corresponds to what ratio in sound intensities of the noise to the music?
(5)


88.     The magnitude of an earthquake, M, is generally measured on the Richter scale and is given as:


where E0 = 104.40 joules. (Note, in class we defined M in terms of intensity not energy so the equation is somewhat different.)
  1. This value for E0 is unusual in that it is expressed in a form useful for computation but not expressed in ordinary scientific notation. What is this value in scientific notation; that is, as d.ddddx10p joules?
    (5)
  2. One of the largest recorded earthquake was in Japan in 1933, with an energy release estimated to have been 5.62x1017 joules. What was its magnitude on the Richter scale?
    (5)
  3. The 1971 earthquake that devastated San Fernando Valley was estimated to have been 6.6 on the Richter scale. What was the energy released in this event?
    (5)
  4. The 1906 earthquake that devastated San Francisco was estimated to have been 8.3 on the Richter scale. In 1989 another major earthquake damaged the San Francisco bay area. It measured 6.9 on the Richter scale. How many more times was the energy released in 1906 as compared to 1989?
    (5)

89.     The brightness of stars is expressed in terms of magnitudes on a numerical scale that increases as the brightness decreases; that is, a brighter star has a smaller magnitude. The magnitude m is given by:

where L is the brightness of the star and Lo is the brightness of the dimmest stars visible to the naked eye.
  1. What is the magnitude of the dimmest star visible to the naked eye; that is, with a brightness of Lo?
    (5)
  2. The typical brightest stars have a brightness of 100 times the dimmest stars; that is, with L = 100 Lo. What is the magnitude of a typical bright star?
    (5)
  
© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner