Extra Credit Problems
Second Quarter

 Instructions:
  1.  Problems may be submitted any time during the six weeks, but they MUST be turned by the due date.  
       (Due Date:  December 3, 2010)
  2.  Your work must accompany each problem.  No credit will be given for just an answer.
  3.  Parts of problems are worth anywhere from 1 - 3 points depending on level of difficulty.
       Credit is given only for correct work and answers. The whole part must be correct to
       receive credit.
  4.  You may do as many or as few problems as you desire. Try to keep them in order.

Problems:

1.   Two trains leave Kansas City at the same time. Train A is traveling due north at 55 mph,
      Train B is traveling west at the rate of 65 mph. Find the distance between the two trains two
      hours later and the bearing of Train B from Train A.

2.   A tree is 18 ft from a house. From the top of the tree, the angle of depression to the base of
      the house is 41o, and the angle of elevation to the top of the house is 26o. Find the height of
      the house.

3.  Graph      without a calculator.
                            

4.  Graph   without a calculator.
                      

5.  Analyze and graph , identifying all local maximum and minimum points
     and asymptotes.   Calculator output is not acceptable.

6.  A salt shaker is sitting 4 centimeters from the center of a lazy Susan. Phoebe Small spins the
     lazy Susan through an angle of 120o.
     a.  Through how many radians does the shaker turn?
     b.  What distance does the shaker travel?
     c.  If Phoebe turned the lazy Susan 120o in 1/2 second, what was the shaker's velocity in
          radians/second?
     d.  What was the shaker's linear velocity? (cm/second)

7.  A small pulley 6 centimeters in diameter is connected by a belt to a larger pulley 15
     centimeters in diameter. The small pulley is turning at 120 rpm.
     a.  Find the angular velocity of the small pulley in radians per second.
     b.  Find the linear velocity of the rim of the small pulley in centimeters per second.
     c.  What is the linear velocity of the rim of the large pulley?
     d.  Find the angular velocity of the large pulley in radians/second.
     e.  How many rpm is the large pulley turning?


8.  Simplify each of the following:

  1. log232
  2. (-3)log-35
  3. 7 log7 (a + 3)
  4. log168
  5. \/2 log43
9.  Radioactive Iodine with a half-life of 8.1 days is used to determine if people have a thyroid
       deficiency. An amount, N, of the Iodine is injected into the blood stream and is absorbed by
       a healthy thyroid gland. By measuring the thyroid's radioactivity at various later times, it is
       possible to tell whether or not the thyroid is functioning normally. Express in terms of N, the
       amount of radioactive Iodine which should be present in a healthy thyroid gland 6 days after
       it was injected into the blood stream.

10.  Given a population of 10,000,000 and an annual growth rate of 3%, how long will it take
       this population to double? Will the population quadruple in twice this doubling time? What is
       the size of the population in triple the doubling time?

11.  For Martha's birthday present her parents presented her with a bank account with $16,000
       in it. When she was born, her parents had placed $2000 in a savings account which was
       guaranteed to double every eight years. How old is Martha?

12.  What exponential function of the form y = aebx goes through the points (3,10) and (6,50)?

13.  The surface area of the Earth is approximately 197 million square miles, including oceans.
        If the population of the Earth is approximately 4.9 billion people, how much room does
        each person have? Suppose the doubling time for the world's population is approximately 41
        years, when did each person have 1 square mile?

14.  A microcomputer system which currently sells for $1100 sold in 1982 for $1850. Assume
       that the cost continues to decrease and that this decrease is exponential.

  1. Derive an equation for the cost based on time since 1982.
  2. Use this equation to predict the cost at the end of one more year.
  3. When will the price fall to $500?
15.  The woods north of town have two types of rabbits. The light brown, fuzzy ones have a
       current population of 300 and doubles the population every 1.4 years. The second kind of
       rabbit is dark brown with pink ears. Its initial population is 1560 and the population doubles
       every 2.5 years. How long before the colonies are the same size?