Math Quiz5

MATH 107 Quiz 5 NAME_______________________________

Instructor: K. Chavis

INSTRUCTIONS

· The quiz is worth 100 points. There are 8 problems (points for each problem is listed).

· This quiz is open book and open notes , unlimited time . This means that you may refer to your textbook, notes, and online classroom materials, but you may not consult anyone . You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our course schedule of the syllabus.

· You must show your work on problems that indicate to show work to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor. Please type your work in your copy of the exam, or if you prefer, create a document containing your work. Scanned work is acceptable also. Be sure to include your name in the document.

· To complete your quiz, you may type your work or scan your hand written work or take pictures of your handwritten work. Once you have completed the quiz, submit your work in your LEO Assignment Folder.

· If you have any questions, please contact me by e-mail ( [email protected] ) and make sure you include Math107 as your subject.

At the end of your exam you must include the following dated statement with your name typed in lieu of a signature.  Without this signed statement you will receive a zero.

I have completed this exam myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this exam.

Name:                                                           Date:

SHORT ANSWER. Answer the questions in the spaces provided. Show all work where indicated.

1. (10 pts) Convert to a logarithmic equation: 6x = 7776. (no explanation required)

2. (12 pts)

(a) _______ (fill in the blank)

(b) Let State the exponential form of the equation.

(c) Determine the numerical value of , in simplest form. Work optional.

3. (10 pts) Which of these graphs represent a one-to-one function? Answer(s): ____________

( no explanation required .) (There may be more than one graph that qualifies.)

(A)

(B)

(C)

(D)

4. (10 pts) A human memory model is used to determine the percentage, M(t), of information that students remember months after the completion of a course. For a specific geography course, students followed the model

a) What percentage of material did the students remember after 8 months? Show work.

b) How many months after the semester did students still remember 45 percent of the material from the course? Show work.

5. (10 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.

6. (10 pts) Let f (x) = 3x2 – 4x – 2 and g(x) = 2x + 1

(a) Find the composite function and simplify the results. Show work.

(b) Find . Show work.

7. (20 pts) Let

(a) Find f – 1 , the inverse function of f. Show work.

(b) What is the domain of f ? What is the domain of the inverse function?

(c) What is f (2) ? f (2) = ______ work/explanation optional

(d) What is f – 1 ( ____ ), where the number in the blank is your answer from part (c)? work/explanation optional

8. (18 pts) Let f (x) = e x – 2 + 3.

Answers can be stated without additional work/explanation.

(a) Which describes how the graph of f can be obtained from the graph of y = ex ? Choice: ________

A. Shrink the graph of y = ex horizontally by a factor of 2 and shift up by 3 units.

B. Reflect the graph of y = ex across the x-axis and shift up by 1 unit.

C. Shift the graph of y = ex to the left by 2 units and up by 3 units.

D. Shift the graph of y = ex to the right by 2 units and up by 3 units.

(b) What is the domain of f ?

(c) What is the range of f ?

(d) What is the horizontal asymptote?

(e) What is the y-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth).

(f) Which is the graph of f ?

GRAPH A GRAPH B GRAPH C

9)

In Exercises 1 - 33, solve the equation analytically.