Answers to the sample test!!

1)  Simplify each:
                     a)  4 . 2-4 =                     b)  (4 . 2)-4 =              c)  (a-1 + b-1)-2 =
                                       4(1/16)                           = 1/84                         (1/a + 1/b)-2
                            = 1/4                            =  1/4096                   = [(a + b)/ab]-2
                                                                                                   =[ab/(a + b)]2
                                                                                                  = a2b2/(a + b)2


2)  Simplify each:
 
 
  a)  (25/9)1/2 = 5/3                  b)  161/2 = 4                    c)  x - 2


3)  Solve the equation:  93x = 81x + 1
                                                          93x = 92(x + 1)
                                                3x = 2(x + 1)
                                        3x = 2x + 2
                                           x = 2


4)  The half life of a radioactive isotope is 7 days.  If 5.6 kg are present now, how much will be present in t days?  In 13 days?
  A(t) = 5.6(1/2)t/7
A(13) = 5.6(1/2)13/7 = 1.55 kg


5)  A bacteria colony triples every 6 days.  The population currently is 5000 bacteria.  What will be the population in 21 days?
  A(21) = 5000(3)21/6 = 233827


6)  $1000 is invested at 8% compounded quarterly for 3 years.  How much interest will you receive at the end of the time period?
  A(3) = 1000(1 + .08/4)12 = $1268.24


7)  You invest $3000 at 7% compounded continuously for 2 years.  How much money will be in the account at the end of the time period?
  P(2) = 3000 e.14 = $3450.82

8)  Solve each log equation:
                 a)  Log x = 21
            Write exponentially,           1021 = x


                 b)  Log |x| = 15
                        Write exponentially and solve: | x | = 1015
                                                                                                            x = 1015 or -1015

 
                 c)  Ln (x2 - 1) = 3
                                Write exponentially and solve
e3 = x2 - 1
e3 + 1 = x2
                                                          _____
+ \/ e3 + 1  = x

 
                 d)  Log x = 1.6  (Use calculator and round to hundredths.)
  Write exponentially,  101.6 = x
                                     x = 39.81

 
9)  Write each log as a single log:
 
                 a)  Log x + log y + 2Log z
                                              =Log xyz2


                 b)  Ln x + Ln y - 3Ln z
                          =  Ln (xy/z3)

10)  Simplify each log:
 
                 a)  Ln e5 =     5
 
                 b)  102log4 =   16
 
                 c)  101 + log 5 = (10)(10log 5) = (10)5 = 50

 
11)  Solve the equation:  Log (x + 2) + Log 5 = 4
Log 5(x + 2) = 4
5(x + 2) = 104
5x + 10 = 10000
5x = 9990
x = 1998

12)  Graph y = 3x and y = log3 x on the same axis.
  


13)  Use a calculator to find Log7 58 and round to hundredths place.
  = log 58/log 7 = 2.09


14)  Solve the equation:  15x + 1 = 29 and round to hundredths place.
  (x + 1)log 15 = log 29
x log 15 + log 15 = log 29
xlog 15 = log 29 - log 15
x = (log 29 - log 15)/ log 15
x = .24


15)  How long will it take to double $1000 if invested at 6% compounded monthly?
 
2000 = 1000(1 + .06/12)12t
2 = (1 + .06/12)12t
log 2 = 12t log (1 + .06/12)
log 2/ 12log(1 + .06/12)  = t
11.58 = t
11.58 years


 
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