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1 Printed Name: Section #: Instructor: Please do not ask questions during this eam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the correct answer. Refer to the last page for general directions and calculator troubleshooting tips. Any communication with any person (other than the instructor or the designated proctor) during this eam in any form, including written, signed, verbal or digital, is understood to be a violation of academic integrity. All devices, such as computers, cell phones, cameras, watches and PDAs must be turned off and stowed away while the student is in the testing room. The only calculators to be used are TI-83, TI-83+, or TI-84+. You may NOT borrow or share a calculator with another person taking this test. Statement of Academic Integrity: I have not and will not give or receive improper aid on this test. In signing below, I acknowledge that I have read, understand, and agree to these testing conditions. Student s Signature: (This test will not be accepted for grading unless it bears the signature of the student.) FR#1 FR #2 FR #3 FR #4 FR#5 FR#6 Scantron Free Response Total Multiple Choice Total Total Possible Points Points Earned Page 1/11

2 MULTIPLE CHOICE: 62 points Use a #2 pencil and completely fill each bubble on your scantron to answer each multiple choice question. (For future reference, circle your answers on this test paper.) There is no penalty for guessing on multiple choice. If you indicate more than one answer, or you leave a blank, the question will be marked as incorrect. Each question is worth 3 points, unless otherwise indicated. D C B C A D C A B B A D A B D A D A B B D A C C B Use the following to answer the net two questions. ct ( ) = t thousand miles gives the mileage on a car, t years since 2008, 0 t Write the following using function notation: In 2014, the mileage on the car was 104,192 miles. a. c (14) = b. c (2014) = 104,192 c. c (6) = 104,192 d. c (6) = Identify the output description and units for the above model. a. the number of years since 2008 b. the mileage increases by 12,605 miles each year c. the car mileage in thousand miles d. between the years 2008 and Which ONE of the following is NOT a representation of a function? a. y = e + ln( ) b y c. The perimeter of a square is four d. times the length of a side. 4. p ( ) represents the proportion of American homes with computers, years after 1999, and nn() represents the number of American homes, years after Which one of the following functions C ( ) represents the number of American homes with computers, years after 1999? a. C ( ) = np ( ( )) b. C ( ) = p ( ) n ( ) c. C ( ) = p ( ) n ( ) d. p ( ) C ( ) = n ( ) Page 2/11

3 5. D ( ) gives the number of PhDs awarded to domestic students by American universities, years after I( ) gives the number of PhDs awarded to international students by American universities, years after Which one of the following models is INCORRECT? a. g ( ) = D ( ) I ( ) gives the percentage of PhDs awarded to domestic students at American universities, years after b. g ( ) = D ( ) I ( ) shows how many more PhDs were awarded to domestic students by American universities than to international students, years after c. g ( ) = D ( ) + I ( ) is the total number of PhDs awarded by American universities, years after d. D ( ) g ( ) = shows the proportion of domestic to international PhDs awarded by American I( ) universities, years after Use the given information for the net two questions. [2 pts each] vt () gives the number of daily visitors to Myrtle Beach t days after June 1, 0 t 90. Rv () thousand dollars gives the daily revenue for Myrtle Beach businesses on a day in which there are v visitors to Myrtle Beach, 1,000 v 50, In the contet of this question, which operation would produce a valid constructed function? a. Addition b. Multiplication c. Division d. Composition 7. What are the proper input and output units for the newly constructed function from the previous question? a. Input units: days Output units: thousand visitors b. Input units: visitors Output units: thousand dollars per visitor c. Input units: days Output units: thousand dollars d. Input units: visitors Output units: thousand dollars Page 3/11

4 8. The function graph below can be used to model the data of current average home values, for homes between 850 sq ft and 1700 sq ft. in size, in Berlin Heights, Ohio. Use the graph to find a completely defined model for the data. a. V( ) = thousand dollars gives the current average home value of a home in Berlin Heights, Ohio of size square feet, b. V( ) = square feet gives the size of a home, where thousand dollars is the current average home value of a home in Berlin Heights, Ohio, c. V( ) = thousand dollars gives the current average home value of a home in Berlin Heights, Ohio of size square feet, d. V( ) = square feet gives the size of a home, where thousand dollars is the current average home value of a home in Berlin Heights, Ohio, Ironman competitors swim and bike for several miles before beginning a marathon run. dt ( ) = 0.148t miles gives the total distance completed by Daniela Ryf in the 2018 Ironman World Championship, t minutes after starting the marathon portion of the race, 0 t 177. Complete the following sentence of interpretation for the slope of the given function. Between the start and the end of the marathon portion of Daniela Ryf s race, the total distance she completed in the entire Ironman competition. a. increased by miles b. increased by miles per minute c. was miles d. increased by minutes per mile Page 4/11

5 10. Which one of the following is TRUE for LINEAR functions defined on the interval (, )? a. They have one concavity. b. They have constant rate of change. c. They have constant percentage change. d. They may have a maimum or a minimum value. 11. [2 pts] Which one of the following scenarios would best be modeled with a LOGARITHMIC function? a. The size of a tree that increases more and more slowly over time. b. The speed of a car after stepping on its brakes, over time. c. The distance a snail has travelled while maintaining a constant speed, for several minutes. d. The amount of money in a bank account that earns a certain percentage of its balance in interest each year, over several years. 12. Which one of the following statements is FALSE regarding logarithmic functions of the form f( ) = a+ bln( )? a. Logarithmic functions always increase or decrease without bound, as input increases without bound. b. Logarithmic functions always have one concavity. c. The graph of a logarithmic function always has a vertical asymptote. d. The graph of a logarithmic function always has a horizontal asymptote. 13. A stock was initially bought for dollars per share. Over a five year period, the value of the stock decreased by 1.5% each year. Complete the following model. s ( ) = bought, 1 5. dollars per share gives the value of a stock, years after it was a (0.985 ) b c (1.015 ) d (0.5 ) 14. Assume gh ( ) = 2 h and Evaluate gh ( (2)). h = can be composed as a newly constructed function, gh ( ( )). 3 ( ) 4 a. 2 b. 4 c. 8 2 d Page 5/11

6 Use the given information for the net two questions. rt ( ) = (0.891 t ) thousand dollars gives the resale value of a boat, t years after it is purchased, 1 t Find the constant percentage change for the model and complete the following sentence. Between one and ten years after the boat was purchased, the resale value of the boat was decreasing by percent per year. a b c d Which one of the following statements correctly describes the graph of rt ()? a. It has a horizontal asymptote. b. It has a vertical asymptote. c. The graph is increasing. d. The graph is concave down. 17. Which function(s) have ALL three of the features below? End behavior increases or decreases without bound as input values increase An inflection point eists No horizontal asymptotes a. Cubic and Logistic b. Linear and Logistic c. Quadratic d. Cubic Only 18. Which of the following functions has a graph with lim f( ) = and lim f( ) =? a. 2 f ( ) = a + b + c, a = 4 b. f a b c d a 3 2 ( ) = + + +, = 2 c. f ( ) = a + b, a = 1.25 d. f( ) = 2( a ), a= 1.5 Page 6/11

7 Which one of the following is the equation for a horizontal asymptote of R ( ) = e? + a. y = b. y = c. y = 1 d. y = Use the graph to answer the net four questions. [1 pt each] 20. Which one of the following is TRUE for the function graphed above? a. lim f( ) = 1 b. lim f( ) = c. + 1 lim f( ) = 0 d. 1 lim f( ) = Which one of the following is TRUE for the function graphed above? a. lim f( ) = b. lim f( ) = c. lim f( ) = d. lim f( ) = Which of the following is a horizontal asymptote? a. y = 0 b. y = 1 c. = 1 d. = 0 e. none eists 23. Which of the following is a vertical asymptote? a. y = 0 b. y = 1 c. = 1 d. = 0 e. none eists Page 7/11

8 Use the following to answer the net two questions. [2 pts each] A student decided to start a rumor on Day 1. The table below shows the number of students in the class who knew the rumor on several days. Day Students who knew rumor Based on a scatterplot of the above data, a logistic model is appropriate, but a cubic model is not. Choose the reason to use a logistic function instead of a cubic function when modeling this data. The reason to choose a logistic function over a cubic function is because the scatterplot. a. shows a change in concavity b. represents an increasing function c. has end behavior indicating two horizontal asymptotes d. appears to have a vertical asymptote 25. It appears that there eists a day where the number of students who knew the rumor was increasing most rapidly. This can be verified on the scatterplot by taking note of. a. the apparent end behavior b. the change in concavity from concave up to concave down, as input values increase c. the change in concavity from concave down to concave up, as input values increase d. the maimum value FREE RESPONSE: 38 points Show work where possible. Read the directions at the front of the test on rounding, inclusion of units, and writing models and sentences. 1. An ice cream shop has daily fied costs of $750 and variable costs of $1.25 per milk shake served. Milk shakes are sold for $5 each. How many milk shakes must be sold to break-even in a given day? Show work and include units with the answer. R ( ) = C ( ) 5= = 750 = milkshakes ( / 3pts ) Page 8/11

9 2. Zach decided to go scuba diving. The following data describes his distance below surface level at various times after jumping in the water. Time, in seconds Distance below surface level, in meters a. Look at scatter plot of the data. How many concavities are suggested by the scatter plot of the data? Circle one: b. Write a completely define logarithmic model for the data. dt ( ) = ln( t) meters gives Zach s distance below surface level while scuba diving, t seconds after jumping in the water, 5 t 45. Part a) 1 pt Part b) 4 pts function equation 1 pt output units 1 pt output description 1.5 pt input units and description 0.5 pts input data range ( / 9 pts ) 3. Ct = t + t+ thousand dollars gives the size of the average US homeowner s 2 ( ) insurance claim paid by the insurance company, t years after (the end of) 1997, 0 t 16. a. Find Ct () when t = 8. Write a sentence of interpretation. C (8) = In 2005, the average US homeowner s insurance claim paid by the insurance company was thousand dollars b. Part (a) uses interpolation/ etrapolation (circle one). c. Use the model to complete the following sentence: Ct ( ) = 8.5 t = So years after the end of 1997 is in the year Checkpoint: C (2) = Part a) 5 pts Part b) 1 pt Part c) 2 pts According to the model, the size of the average US homeowner s claim paid by the insurance company will first reach 8,500 dollars years after (the end of) 1997, in the year (round answer to 3 decimal places) (specify the year) ( / 8 pts ) Page 9/11

10 4. Use the function 0.5 f( ) = 1+ to answer the following. checkpoint: f (2) = a. Use the following table to numerically estimate lim f( ) for f( ) = 1 +. Round each value in the table to three decimal places. Round the limit to three decimal places. f( ) Part a) 2.5 pts Part b) 1.5 pts , lim 1 + = _ _ b. Does the limit in part a) describe a vertical asymptote or a horizontal asymptote? (circle one) Write the equation of the asymptote. y = _ ( / 4 pts ) 5. The data in the table below shows temperatures in both Fahrenheit and Celsius and can be used to find a linear function CF ( ). Find the inverse of CF ( ): F degrees Fahrenheit C degrees Celsius C degrees Celsius F degrees Fahrenheit a. Complete the table to the above right to use in finding the inverse function, FC ( ). b. The linear equation of the inverse function is FC ( ) = 1.8C Part a) 1 pt Part b) 2 pts ( / 3pts ) Page 10/11

11 6. Consider the graph of f( ) below to answer the following questions. Part a) 6 pts Part b) 1 pt Part c) 1 pt Part d) 2 pts a. Fill in the blanks. A limit must specify a number,,, or DNE (if the answer does not eist or is undefined). f (2) = 1 lim f( ) = 1 lim f( ) = 3 lim 2 f( ) = dne lim f( ) = lim 3 f( ) = 6 b. Is the function f( ) is continuous at = 2? No (Yes/ No) If no, indicate the reason by circling the first of these three reasons that is not satisfied. f (2) is undefined (does not eist) lim f( ) does not eist 2 lim f( ) 2 f (2) c. Is the function f( ) is continuous at = 3? Yes (Yes/ No) If no, indicate the reason by circling the first of these three reasons that is not satisfied. f ( 3) is undefined (does not eist) lim f( ) does not eist 3 lim f( ) 3 f ( 3) d. On the interval (,0), the function is decreasing, increasing, constant (circle one). On the interval (,0), the function is/has concave down/concave up/no concavity (circle one). ( /10 pts ) 7. A scantron correctly bubbled with a #2 pencil, a correctly-bubbled XID, a correctly-bubbled test version, AND a signed academic integrity statement (on the front of the test) earns 1 point. --- END OF TEST --- Page 11/11

12 General Directions: Show work where possible. Answers without supporting work (where work is appropriate) may receive little credit. Do not round intermediate calculations. Answers in contet ALWAYS require units. Assume end of the year data unless stated otherwise. Round your answers to 3 decimal places UNLESS the answer needs to be rounded differently to make sense in the contet of the problem OR the directions specify another type rounding OR the complete answer has fewer than 3 decimal places. When asked to write a model, include all components of a model: an equation, a description of the input including units, a description of the output including units, and the input interval when known. When asked to write a sentence of practical interpretation, answer the questions: when?, what?, and how much? using ordinary, conversational language. DO NOT use math words, terms, or unnecessary phrases. Always use a ruler when estimating values off of a graph. HINTS FOR TROUBLESHOOTING YOUR CALCULATOR: If you lose your L1, L2, etc., you may reinsert them using STAT 5 (set-up editor) enter. The SCATTER PLOT will not show unless Plot 1 has been turned on and there is data in L1 and L2. ZOOM 0 may not work for graphing if Plot 1 is turned on. DIM MISMATCH error usually means that the lists in L1 and L2 are not of equal length. DATA TYPE error usually means that you already have something in Y1 and you need to clear it before you can paste a new equation. INVALID DIM error usually means that your plot(s) are on, but that you have no data in the lists. Refer to the second hint above. If your batteries die, raise your hand and hold up your calculator. If your instructor has an etra calculator available, he/she will loan it to you for a few minutes. SYNTAX ERROR: Try GO TO. This will happen if you use a subtraction minus sign when you should use a negative sign. MATH SOLVER only works if there is a variable in Y1. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 12/11