Math 110                                                                                               Name: ______________________________

Exam V: Chapters 6 and 7, Exam IV                                   Date:   ______________________________

Directions: Show all steps for full credit.  Round all answers to the hundredths place.

Part I: Only scientific calculators allowed.

For problems #1 - #5, solve the equations using any symbolic method of your choice:  

     1.         

     2.         

     3.         

4.               

    5.       

6.     Evaluate  without using your calculator. Show all work.

7.      Rationalize the denominator:   

8.     Find the inverse equation for the given function. Show steps!        

9.   Answer the following miscellaneous questions:

     a.    What is the value of ?                                                             ___________

b.       What is the equation of the line that lies between

             the graphs of  two inverse functions?                                 ___________

     c.    What is the base of a natural logarithm?                                             ___________

     d.     How is expressed using radicals?                                               ___________

     e.     How is expressed using a rational exponent?                         ___________

For problems #10 - #16, SIMPLIFY each expression.

10.                                                     

11.     

12.        

13.                                         

14.                                       

15.         

16.            

                                                                                                                Name: ______________________________

Part II: Graphing calculators allowed.

17.   Give the information for the function below. You may want to draw a rough sketch first.

Domain:                                                                                 ______________________________                   

Range:                                                                                    ______________________________

exponential growth or decay  (choose one)                       ______________________________

x-intercept point                                                                   ______________________________

y-intercept point:                                                                  ______________________________

Equation of horizontal asymptote:                                     ______________________________

18.   Give the information for the function below. You may want to draw a rough sketch first.

Domain:                                                                                 ______________________________                   

Range:                                                                                    ______________________________

x-intercept point                                                                   ______________________________

y-intercept point:                                                                  ______________________________

increasing or decreasing everywhere?                              ______________________________

Equation of vertical asymptote:                                          ______________________________

EXTRA CREDIT

A college loan of $29,000 is made at 8% interest, compounded annually. After t years, the amount due, A,  is given by the function  .

a)       After what amount of time will the amount due reach $40,000? Show work.

b)       After what amount of time will the amount due be double the initial loan amount? Show work.