1090fall08 final by de443B3

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									Name ______________________                MATH 1090          FINAL EXAM               instructor:                         .
date              Dec. 2008                                                                          2 hours with calculator
section / time:               .
         Work problems completely, either on this paper, or on another sheet, which you include with this paper.
         Credit will be given for work, so show all necessary work. If you turn in work on another paper, number the
         problems so they can be found and read. If you answer “none of the preceding,” tell what the answer should be.

                      Work 15 of the18 problems on this exam. Mark out the 3 problems
                      that will not be graded. The first 15 not marked out will be scored.

1. The resident population of Florida (in thousands) is given in the table at the right. Let x equal the
   number of years after 1980 and y equal the number of thousands of residents. Identify the linear
   model that is the best fit for this data.                                                     Population
                                                                                      Years
                                                                                                 (thousands)
    a) y = 168.92x + 10,642.32             b) y = 285.27x + 9875.17                   1980          9,746
                                                                                      1985         11,351
    c) y = 285.27x – 12,946.37             d) y = 3.5x2 + 350x + 9732                 1990         12,938
                                                                                      1995         14,180
    e) y = 9970.32(1 + 0.023) x            f ) None of the preceding.                 1996         14,425
                                                                                      1997         14,677
                                                                                      1998         14,916

2. At the end of an advertising campaign, weekly sales declined according to the equation
   y = 10,000(3–0.05x) dollars, where x is the number of weeks after the campaign ended.
   Determine the sales at the end of the campaign, and 8 weeks after the end?

    a) end $0, 8-weeks $7572                  b) end $10,000, 8-weeks $6444             c) end $0, 8-weeks $6444

    d) end $10,000, 8-weeks $8452             e) end $10,000, 8-weeks $7572             f ) None of the preceding.




3. The average price of a U.S. movie ticket is given in the                             Ticket                     Ticket
   table. Use a model of this data to make the best estimate                Year                       Year
                                                                                       Price ($)                  Price ($)
   of when the price was $5.70.                                             1991         4.21          1996         4.42
                                                                            1992         4.15          1997         4.59
    a) 2000                                   b) 2001                       1993         4.14          1998         4.69
                                                                            1994         4.18          1999         5.08
    c) 2003                                   d) 2005                       1995         4.35
    e) 2006                                   f ) None of the preceding.
                                                                                                            2
4. A delivery service has three
   types of aircraft, each of                                               Aircraft Type
   which carries three types of Units Carried               Passenger (P) Transport (T) Jumbo (J)
   cargo. The payload of each Next-Day Letters (a)               200             200              200
   type is summarized in the        Two-Day Letters (b)          300              40              700
   table at the right. Suppose      Air Freight (c)               40             130               70
   on a given day the airline
   must move 2200 next-day delivery letters, 3860 two-day delivery letters, and 920 units of air freight.
   Identify the system that tells how many aircraft of each type should be scheduled.

       200a  300b  40c  2200                          200x  200 y  200z  2200
                                                         
    a) 200a  40b  130c  3860                       b) 300x  40 y  700z  3860
       200a  700b  70c  920                            40 x  130 y  70 z  920
                                                         

       200P  300T               40 J    2200          200a  200b  200c  2200
                                                         
    c) 200P  40T            130J        3860       d) 300a  40b  700c  3860
       200P  700T                                      40a  130b  70c  920
                                  70 J       920         

       200P  200T           200 J       2200
       
    e) 300P  40T            700 J       3860       f ) None of the preceding.
        40 P  130T                     
                                  70 J       920




5. Suppose a long-distance call costs 99¢ for the first minute plus 25¢ for each additional minute.
   Identify the equation that gives the cost C of a call lasting n minutes.

    a) C(n) = 0.99 + 0.25(n – 1)          b) C(n) = 0.99 + 0.25n             c) C(n) = 0.99 + 0.25n

    d) C(n) = 0.99 + 0.25(n – 1)          e) C(n) = 0.99 + 0.25(n + 1)       f ) None of the preceding.




6. A loan of $36,000 is to be amortized with monthly payments over 6 years. If the interest on the
   loan is 6% per year, paid on the unpaid balance, what payment is required each month to amortize
   the loan?

    a) $5925.44                           b) $416.62                         c) $596.62

    d) $6105.44                           e) $311.07                         f ) None of the preceding.
                                                                                                               3
 7. Suppose the demand for artificial Christmas trees is given by the function p = 109.70 – 0.10q and
    that the supply of these trees is given by p = 0.01q2 + 5.91 where p is the price of a tree in
    dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price
    that gives market equilibrium.

     a) $91.60                                b) $97.00                        c) $100.00

     d) $107.00                               e) $120.40                       f ) None of the preceding.




 8. The average cost per unit for the production of a certain brand of DVD players is given by
         400  50 x  0.01 x 2
    C                           where x is the number of hundreds of units produced. Use the
                    x
    graph of this function to find the minimum average cost.

     a) $54                                   b) $55                           c) $100

     d) $200                                  e) $400                          f ) None of the preceding.




 9. Assume the growth of the population of Del Webb’s Sun City Hilton Head community
    northwest of Phoenix was linear from 1996 to 2000, with a population of 196 in 1996
    and a rate of growth of 705 per year. Identify the equation for the population P of this
    community as a function of the number of years x after 1996.

     a) P (x) = 196x + 705                    b) P (x) = 196x + 1996           c) P (x) = 1996x + 705

     d) P (x) = 705x + 196                    e) P (x) = 705x + 1996           f ) None of the preceding.




10. The function that converts euros to U.S. dollars according to Oct. 1, 2008, values is f ( x ) = 1.3816x,
    where x is the number of euros and f ( x ) is the number of U.S. dollars.

     (a) Find f -1( x ), the inverse of f .


     (b) Interpret its meaning.
                                                                                                      4
11. A political candidate wishes to use a combination of television and radio advertisements in his
    campaign. Each 1-minute ad on television reaches 0.18 million
    eligible voters and each 1-minute ad on radio reaches 0.09 million
    eligible voters. The candidate feels that he must reach at least 6.3
    million eligible voters, but that he should use no more that 60
    minutes of advertisements.

      (a) Write the inequalities that describes these advertising
          requirements.




      (b) Graph the region determined by these inequalities in the
          context of the application. (Be sure to make the scale for each axis.)



12. The revenue from the sale of a product is given by the function R(x) = 3000x – 0.15x3 dollars.
    Determine how many units should be sold to give a revenue of at least $150,000.




13.   The percentage of Fortune Global 500 firms that actively recruited workers on the Internet
      from 1998 through 2000 can be modeled by P(x) = 26.5x – 194.5 percent where x is the
      number of years after 1990. Explain why, or why not, this model should be used to
      predict the percentage of Fortune Global 500 firms that actively recruit workers on the
      Internet in 1997.




14.   Rewrite the expression 4 ln(2a) – ln b as a single logarithm.




                                      f x  h   f x 
15.   Find the difference quotient                        when f ( x ) = 3x2 – 2x + 5.
                                              h
                                                                                                                   5
16.    A business plans to use three methods of advertising:
      newspapers (n), radio (r), and cable TV (c) in each of its        Table I      p       r        c
      two markets, Allentown (A) and Brownsville (B). The                  A        16      12        8
      cost per ad type in each market (in thousands of dollars)            B        12      10        9
      is given in Table I. The business has three target groups:
      young single females (x), young single males (y), and
      young married couples (z). Table II gives the number of
      ads per week directed at each of these groups.                     Table II   p        r       c
                                                                             x      4       10      12
                                                                             y      6       14       8
      (a) Write a matrix multiplication that shows how the                   z      8        9       8
          advertising money is spent among the target groups in the
          two markets. (Be sure to label the rows and column in the answer.)




       (b) Use the result of the multiplication in part (a) to tell which market group has the highest cost,
           and tell what that cost is.




17.   The cost C to obtain drinking water that contains p% impurities for the town of Pleasant View is
                                  85,000
      given by the equation C             15,000 . Describe the transformations and/or stretches
                                     p
                                                                             1
      needed to obtain this function from the basic reciprocal function C  .
                                                                             p




18.   If changing market conditions cause a company earning $1,250,000 this year to project decreases
      of 2% of its profit in each of the next four years, what is the sum of its yearly profits that it projects
      for the next four years?
                                                                                                               6

                                         *** ***
Formulas:

           (1  i ) n  1
                                                                                             kt
                                                                                r
     S  R                          S = Pe   rt
                                                                         S  P 1  
                 i                                                            k

     S = P(1 + r) t
                                          1  (1  i) n 
                                      A R                              sn 
                                                                                  
                                                                                a1 1  r n       (if r ≠ 1)
                                                                                 1 r
                                                i        
                      n  a1  an 
              sn                                   an = a1 + (n – 1)d                   an = a1r n – 1
                            2
                                                                                                                      7
                           Answers — Math 1090, FINAL EXAM, Fall 2008

   1. sect’n 1.6, chap-rev #63, b         2. sect’n 3.1, #24, b              3. sect’n 4.2, #29, b
f ) y = –3.5x2 + 350x + 9732 is good answer

   4. sect’n 5.1, chap-rev #39, e         5. sect’n 6.3, #22, d              6. sect’n 3.6, #22, c


   7. sect’n 2.2, #59, c                  8. sect’n 4.5, #30, d              9. sect’n 1.4, #41, d

  10. sect’n 2.7, like # 45,      (a) f -1( x ) = 0.7238x
                                  (b) one U.S.dollar is worth 0.7238 euros        80


                                0.18T            0.09 R        6.3             60
                                
  11. sect’n 6.1, like #27, (a)  T                 R           60              40
                                T           0,   R       0
                                                                                 20
                            (b) —> >          —> graph —> > —>
  12. sect’n 4.6, like #31, 62 ≤ x ≤ 100, between 62 and 100 units,                      20    40        60
                                                                                              # television ads
                                                                                                                 80

                                          inclusive

  13. sect’n 1.3, #39, This model should not be used to predict the percentage of Fortune
                       Global 500 firms that actively recruit workers on the Internet in 1997
                       because the model predict a negative percent which is impossible.


                           16a 4 
                           b 
  14. sect’n 3.3, #25, ln        
                                 

  15. sect’n 1.4, like #34, 6x + 3h – 2
                                                                       4 6 8                  x   y   z
                                                        16 12 8                
                                                                    10 14 9  A           280 328 300
                                                       T
  16. sect’n 5.3, like example #6, (a) [ I ] × [ II ] = 
                                                        12 10 9 12 8 8                    256 284 258
                                                                                  B                    
                                                         T
                                        or [ II ] × [ I ] = same answer, only transposed
                                         (b) The males in Allentown have the highest cost at $328,000

  17. sect’n 2.4, like #42, stretches function 85,000 times, and then shifts function up 15,000 units


  18. sect’n 64, like #28, $4,754,950.20
                                                                                                          8

┌ *   – * –* – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * – * ┐
*      Text Sect’n         test prob #                         Text Sect’n           test prob #     *
|                                                                                                     |
            1.1       -                                              4.1      -
*           1.2       -                                              4.2      -          3           *
|                                                                                                     |
            1.3       -        13                                    4.3      -
*           1.4       -         9, 15                                4.4      -                      *
|                                                                                                     |
            1.5       -                                              4.5      -          8
*           1.6       -         1                                    4.6      -         12           *
|                                                                                                     |
            1.7       -                                              5.1      -          4
*           1.8       -                                              5.2      -                      *
|                                                                                                     |
            2.1       -                                              5.3      -         16
*           2.2       -         7                                    5.4      -                      *
|                                                                                                     |
            2.3       -                                              6.1      -         11
*           2.4       -        17                                    6.2      -                      *
|                                                                                                     |
            2.5       -                                              6.3      -          5
*           2.6       -                                              6.4      -         18           *
|                                                                                                     |
            2.7       -        10
*           2.8       -
|
            3.1       -         2
*           3.2       -
|
            3.3       -        14
*           3.4       -
|
            3.5       -
*           3.6       -         6
|
            3.7       -

								
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