MATH 111 - Final Exam	Name: __________________________________
Fall 1997	Student I.D.# _____________________________

General test instructions: Show all your work on this test paper! If you solve a problem algebraically show all your steps. If you solve a problem by graphing on your calculator, show a sketch of the graph, with the solution labeled. Where appropriate, round answer to 3 decimal places.

1. Solve algebraically and give exact solutions:

2. Solve for x:

    

    

    

   
   Solve the following inequalities, sketch the solution on the real number line:

3. ç 5 - 2x ç < 9

    

    

    

4.  

    

5. Solve:

   7e-.03t = 2

    

    

    

6. Solve:

    

7. Find all points of intersection for the following system of equations:

   

    

    

8. Solve:

   3x - 7y	=	5
   -x + 2y	=	10

   
   
   

9. A 55-gallon barrel contains a mixture with a concentration of 33%. You remove x gallons of this mixture and replace it with the same amount of 100% concentrate. Find the value of x if the final mixture is a 60% concentration.

    

    

   
   
   
    

10. The revenue in dollars from selling x items of a product is . Find the number of units that produces a maximum revenue.

     

     

     

     

      

11. Calculate the amount of money that should be invested at 6% compounded continuously to produce a final balance of $30,000 in ten years.

     

     

     

     

    
    

12. Evaluate (Show your work.)

     

    
    

     

13. Simplify: (3-2i)(4+i). Write your answer in the standard form for a complex number.

     

     

     

     

     

14. The population P of a city is given by P = 10,000 where t = 0 in 1990. In1995 the population was 12000. Find the value of k, and use this value to predict the population in the year 2002.

     

     

     

     

    
    

15. Find an equation of the line that passes through the points (1,6) and (-2,5).

     

     

     

     

     

     

16. Given f(x) = and g(x) = 5x + 2, find (f g)(x).

     

     

     

     

     

17. Given the function, f(x) = what is its

    a) domain?

     

     

    b) range?

     

     

     

     

18. Given f(x) =

    a) Find the inverse function f

     

     

      

    f ^-1(x) = _________________

    b) Graph f(x) and f

     

     

     

     

      

19. Find all the zeros of this polynomial.

    

     

     

     

     

     

20. Given this sketch of a polynomial function:

    

    a) Is it a 3rd degree or 4th degree equation?

    b) Is the leading coefficient positive or negative?

21. Graph the function

    f(x) =

     

     

     

     

     

    
    

22. Graph and. Label any intercepts.

     

     

     

     

     

     

     

23. f(x) is sketched on the axes below. Translate it to sketch a graph of f(x+1) - 3

     

    

     

24. The table below indicates the federal debt in billions of dollars from 1940 to 1990. (Year = 40 is 1940)

    Year	40	50	60	70	80	90
    Debt	51	257	291	381	909	3207

    1. Plot these points on the axes.
    2. Use your graphing calculator to find the least squares regression line for the data. Write your equation and correlation coefficient here.

        

        

        

    3. Use your graphing calculator to find an exponential equation for the data. Write your equation and correlation coefficient here.

        

        

    4. Which is a better model of the data? Why?

        

         

    5. Use the better model to predict the debt in 1995.

     

     

25. For the function, f(x) = give the following:
    1. y-intercept

        

        

    2. x intercepts

        

        

    3. vertical asymptotes

        

        

    4. horizontal asymptote

        

        

    5. graph y = f(x); include x and y-intercepts and all asymptotes.