MAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.

Transcription

1 MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the solution. Where appropriate, round correctly to 2 decimal places. 200 possible points

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3 Fall 2013 MAT 111 Final Exam Name: Score: /200 Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the solution(s). Where appropriate, round correctly to 2 decimal places. 1. [6 pt.] Solve. ( ) 3. [8 pt.] Solve. 2. [6 pt.] Solve. Find the exact value. 4. [8 pt.] Solve the following inequality. Write the solution in interval notation.

4 5. [8 pt.] Solve the following inequality. Write the solution in interval notation. 7. [8 pt.] Solve. ( ) 6. [6 pt.] Solve the system of equations. 8. [8 pt.] Solve algebraically. { ( )

5 9. [6 pt.] Find all real and complex solutions and simplify. 11. Sketch the graphs of the following. (Label all intercepts and asymptotes.) a. [3 pt.] y e x 2 b. [3 pt.] log x y [6 pt.] Write the following as a sum and difference of simple logs (powers as factors). [ ( ) ] 12. Starting with the graph of y f x (pictured) a. [4 pt.] List the transformations necessary to obtain the new function y f x 4. b. [4 pt.] Graph the new function (on the same axes). Label three points.

6 13. The table below lists the amount of money spent by five students at the county fair, compared with the amount of time each student remained at the fair. 14. Given the function ( ) Time at Fair (in minutes) Total Money Spent (in dollars) a. [4 pt.] Using you graphing calculator, decide whether a linear or exponential model is more appropriate. Give a reason for your answer. a. [2 pt.] Find the domain of ( ) b. [2 pt.] Find the x-intercepts. c. [2 pt.] Find the y-intercepts. b. [4 pt.] Express the model of best fit that predicts total money spent, M, as a function of time, t, at the fair. d. [4 pt.] Locate vertical asymptotes. c. [2 pt.] Using the answer to part (b), estimate the money spent for someone who was at the fair for 73 minutes. (to the nearest dollar) e. [2 pt.] Determine horizontal asymptotes. f. [4 pt.] Sketch the graph of ( ) Label all intercepts and asymptotes. d. [2 pt.] Given that a student spent $95, what is the student s approximate time spent walking around the fair. (to the nearest minute)

7 15. Given the function ( ) a. [5 pt.] Find the inverse function ( ) 17. Consider ( ) ( ) ( ) ( ) a. [2 pt.] The end behavior of the graph of ( ) resembles the graph of what power function? b. [9 pt.] Find the zeros and their multiplicities. Zeros Multiplicity Touch or Cross? b. [2 pt.] What is the range of ( ) 16. Given ( ) and ( ) c. [4 pt.] Graph. a. [3 pt.] Find ( )( ). b. [3 pt.] Find the domain of ( )( ) in interval notation.

8 18. Yeast in a sugar solution is growing at a rate such that 2 grams becomes 5 grams after 23 hours. a. [4 pt.] Find the growth constant. 19. Given ( ) +2 a. [2 pt.] Use a graphing calculator to sketch the graph of ( ) b. [2 pt.] Find and label the local maximum point(s). b. [2 pt.] Find the exponential growth function. c. [2 pt.] Find and label the local minimum point(s). d. [4 pt.] On what interval(s) is ( ) decreasing? c. [4 pt.] How long will it take for the yeast to double in size? 20. [6 pt.] Find the equation of the line in slope- intercept form that is perpendicular to and passes through the point ( ).

9 21. [6 pt.] To celebrate the birth of a new daughter, Helen invests $6,000 in a college savings plan to pay for her daughter s first year of college. How much will she have after 18 years of saving if her money is invested at 6% compounded quarterly? 23. Let ( ) { a. [4 pt.] Sketch f (x) labeling key points. 22. [8 pt.] A coffee manufacturer wants to market a new blend of coffee that will sell for $4.19 per pound by mixing Folger s coffee that sells for $2.75 and Colombian coffee that sells for $5.00 per pound, respectively. What amounts of each coffee should be blended to obtain 100 pounds of the desired mixture? b. [2 pt.] Find the domain of f (x). Use interval notation. c. [2 pt.] Find the range of f (x). Use interval notation. d. [2 pt.] ( ) e. [2 pt.] ( )

10 24. The price P (in dollars) and the quantity x sold of a certain product obey the revenue function below. ( ) a. [3 pt.] What quantity x maximize the revenue? b. [3 pt.] What is the maximum revenue? c. [2 pt.] What price should the company charge to maximize the revenue?

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