Practice Exam #3

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					Practice Exam #3 Course: Math-151               Instructor: Julie Tarr
Show your work to receive credit.

1. Using polynomial division, divide 3x 4  10 x3  7 x 2  17 x  3 by 3x  4 and write your
                     r ( x)
   answer in q( x)         form.
                     d ( x)
2. Give the logarithmic expression in exponential form and the exponential expression
   in logarithmic form:
                    2
       a. log 8 4 
                    3
       b. 7  1
             0



3. Using logarithmic properties,
   a) Express ln 2 x  2(ln x  ln w) as a single logarithm and simplify.
                        x3 y
   b) Express ln             as a sum and/or difference of logarithms.
                        a 2b

                                                            2
4. Solve the exponential equation algebraically:  23 x 1   45 x
                                                          

5. Solve the logarithmic equation algebraically: log2 ( x  4)  log2 (4  x)  3.

6. How much money should you invest at 7.5% apr compounded continuously so that
   a) you have $20,000 after 5 years? Show your equation.
   b) How long will it take to double your investment?

7. Suppose that an ounce of food A contains 40 calories, 5 grams of protein, and 30 mg
   of Vitamin C; an ounce of food B contains 200 calories, 2 grams of protein and 10 mg
   of Vitamin C; and an ounce of food C contains 400 calories, 4 grams of protein and
   300 mg of Vitamin C. How many ounces of each group are needed for a meal
   consisting of 600 calories, 25 grams of protein and 425 mg of Vitamin C?
   a) Set up the system of equations for this situation.
   b) Set up the associated matrix.
   c) Find the row-reduced echelon form of this matrix.
   d) Interpret the rref form of this matrix.

           6
8. Find    (10 j  j
          j 2
                        2
                            )

9. Find the first six terms for the recursively given sequence: a1  3; an1  2an  1 .

                                            1   1   1              1
10. Use summation notation to express                             .
                                            2 2 3 3 4         99  100

				
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