Printed Name: Section #: Instructor: Please do not ask questions during this exam. 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 exam 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 Scantron Free Response Total Multiple Choice Total Total Possible Points 8 6 7 5 5 1 32 68 100 Points Earned Page 1/12
MULTIPLE CHOICE: 68 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. 1. [ 2 pts] Which one of the following options describes the graph? a. Concave up, increasing b. Concave down, decreasing c. Concave up, decreasing d. Concave down, increasing Answer the following two questions using the graph below. 2. On what interval(s) is the graph decreasing? a. (, 10 / 3 ),( 0,7 / 3) b. (, 1/ 3) c. (, 2) d. ( 2, 4 / 3) 3. Which one of the following is approximately the x-coordinate of an inflection point? 1 4 7 a. x = b. x = 2 c. x= d. x= 3 3 3 Page 2/12
4. Describe the end behavior of the following graph of f. a. lim f ( x) = 0 and lim f ( x) = 3 b. lim f ( x) = 3 and lim f ( x) = 0 x x x x c. lim f ( x) = and lim f ( x) = d. lim f ( x) = and lim f ( x) = x x x x Use the following graph of the function f ( x ) to answer the next three questions. 5. [2 pts] Find the limit: lim x 2 f ( x) =. a. 8 b. 3 c. -6 d. does not exist 6. [2 pts] Find the limit: lim x 2 + f ( x) = a. 8 b. 3 c. -6 d. does not exist 7. Which one of the following statements is true for the function f ( x )? a. f ( x) is continuous at x= 2. b. f ( x) is not continuous at x= 2 because f (2) is not defined. c. f ( x) is not continuous at x= 2 because lim f ( x) does not exist. x 2 d. The continuity of f ( x ) at x= 2 cannot be determined. Page 3/12
Use the following graph of the function f ( x ) to answer the next two questions. 8. Find the following limit: lim f ( x) =. x a. b. c. 2 d. -5 9. lim f ( x) = and this implies that ( ) x 2 f x has a vertical asymptote at. a., x= 2 b., x= 2 c., y= 2 d. 5, x = 5 10. A study of king penguins found a relationship between how deep the penguins dive to seek food and how long they stay under water. D( x) = 2.915x+ 0.015 yards gives the depth of a king penguin dive, where x is the duration of the dive in minutes, 1 x 9. Complete a sentence of interpretation for the slope of D( x ). When a king penguin dive is between 1 and 9 minutes,. a. the depth of the dive increases by 2.915 yards per minute that it remains underwater. b. the depth of the dive increases by 0.015 yards per minute that it remains underwater. c. the depth of the dive increases by 2.915 minutes per yard. d. the depth of the dive increases by 2.915 yards. Page 4/12
11. [2 pts] A relation is described in the table. Name an ordered pair that could be removed so that the remaining ordered pairs form a function, y as a function of x. a. ( 5,4 ) b. ( 1, 2) c. ( 4,7 ) d. ( 3,1 ) x 1 2 5 1 4 3 y 2 4 4-2 7 1 Use the following to answer the next two questions. The median weight of a female newborn, aged 0 months, is 7.0 pounds. Between 0 and 6 months of age, the median weight of a female infant increases by 1.5 pounds per month. 12. Complete the following model by filling in the blank. pounds gives the median weight of a female infant, t months since birth, 0 t 6. a. W( t ) = 7(1.015 t ) b. W ( t) = 1.5t+ 7 c. W( t ) = 7(1.5 t ) d. W ( t) = 7t+ 1.5 13. [2 pts] Fill in the blanks to the following sentence. Finding the median weight of a 5 month old girl with the above model uses and finding the weight of a 7 month old girl uses. a. interpolation; interpolation b. extrapolation; extrapolation c. extrapolation; interpolation d. interpolation; extrapolation 14. Albuterol is used to calm bronchospasm. It is typically inhaled in a 1.25 mg dose. The amount of albuterol left in the body decreases by 9.4 percent each hour. Find an equation to complete the model. mg gives the amount of albuterol left in the body x hours after an initial dose, 0 x 12. x x a. A( x= ) 1.25(0.906 ) b. A( x= ) 9.4(1.25 ) x c. A( x) = 9.4x + 1.25 d. A( x= ) 1.25(1.094 ) Page 5/12
Use the following to answer the next two questions. The population of a town in various years is given in the table below. Year 1990 1991 1992 1993 1994 Population, in thousands 5.093 6.871 9.278 12.542 16.917 15. Align the data to the number of years after 1990. A function that models the data, after the data was aligned to the number of years after 1990, is given. Complete the model for the aligned data. x P( x= ) 5.091(1.350 ). a. thousand people gives the population x years after 1990, 1990 x 1994. b. thousand people gives the population in year x, 1990 x 1994. c. thousand people gives the population x years between 1990 and 1994. d. thousand people gives the population x years after 1990, 0 x 4. 16. According to the model, which one of the following statements describes the constant percentage change in the town s population? Between the years 1990 and 1994, the population of the town. a. is increasing by 1.35% per year b. is increasing by 5.09% per year. c. is increasing by 35% per year d. is increasing by 65% per year. 17. For the first quiz of the semester, an instructor figured out that the total time spent grading p student papers was t( p) = 2 p+ 3 minutes, where p represents the number of papers graded,1 p 30. How is this function represented? a. Numerically b. Algebraically c. Graphically d. Verbally Page 6/12
Use the following to answer the next two questions. A small beach-side resort hotel uses seasonal pricing for its rooms to remain competitive during the busy summer months. th P( t ) hundred dollars per room is the price for a room for one night during the t month, 1 t 12. For instance, January is t= 1. th N( t ) rooms is the average number of occupied rooms during the t month, 1 t 12. For instance, January is t= 1. 18. [2 pts] What is the hotel s revenue for one night in July? a. P(7) + N (7) b. P( N (7)) c. P(7) N(7) d. N ( P (7)) 19. [2 pts] What are the units for the function that gives the hotel s revenue for one night in July? a. hundred rooms b. dollars c. dollars per room d. hundred dollars Use the following to answer the next two questions. Jennifer is training for a marathon that takes place in six months. h( x ) hours gives the cumulative amount of time Jennifer spends running, x weeks since the start of training for the marathon, 0 x 26. C( h ) calories is the number of calories burned while running for h hours, 0 h 125. 20. [2 pts] How can the two functions be combined to make a meaningful new function? a. multiplication, C( h) h( x) b. composition, C( h( x )) c. division, C( h) / h( x ) d. composition, h( C( x )) 21. [2 pts] What units will the new function have? a. hours b. calories c. calories per week d. calories per hour Page 7/12
22. P( t ) million dollars gives a company s profits t years since 2000 while C( t ) million dollars gives the company s total costs t years since 2000. Which one of the following equations has a solution that gives the break-even point? a. P( t ) = 0 b. P( t) = C( t) c. C( t ) = 0 d. P( t) = t 23. Find the linear function that is an inverse to W( L) using the nasal measurements of a gray kangaroo presented in the table below. L, Nasal Length (mm) 609 620 629 W, Nasal Width (mm) 222 233 241 L( W ) = mm is the nasal length of a gray kangaroo when W is its nasal width, 222 W 241 a. L( W ) = 701.013 + 242.436 ln( W ) b. L( W ) = 0.942L + 815.326 c. L( W) = 1.049W+ 375.861 d. L( W ) = 375.861W 1.049 24. Which of the following statements is TRUE concerning the graph of 3 2 f ( x) = 2x 4x 8? a. lim f ( x) = and lim f ( x) = b. lim f ( x) = and lim f ( x) = x x x x c. lim f ( x) = and lim f ( x) = d. lim f ( x) = and lim f ( x) = x x x x 25. Which of the following statements is TRUE concerning the graph of 2 f ( x) = 3x + 6x 10? a. It achieves a minimum value. b. It achieves a maximum value. c. It has two concavities. d. lim f ( x) = and lim f ( x) = x x Page 8/12
26. [2 pts] Which one of the following limits is suggested by the table? a. b. lim f ( x) = - x 1 x 1 lim f ( x) = - + c. lim f ( x) = 1 x d. lim f ( x) = -1 x x f ( x ) 0.9-15.100 0.99-195.000 0.999-1995.000 0.9999-19,995.000 0.99999-199,995.000 FREE RESPONSE: 32 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. The table below shows cumulative box office revenues on various days after the June 4, 2004 release of the movie: Harry Potter and the Prisoner of Azkaban. Days after release,t Cumulative Box Office revenues, R, in thousand dollars 1 5 16 30 50 80 38.268 109.363 185.308 221.403 240.500 246.901 a. Look at scatterplot of the data. How many concavities does it show? (Circle the answer.) no concavity/ one concavity/ two concavities b. Find a logarithmic function to model the data and write a completely defined model. ( /8pts) Page 9/12
157.345 2. Consider the following function: f ( x) = 1.895 1 + 12.275e x Checkpoint: f (2) = 123.17974 a. The graph of f ( x) is increasing/ decreasing (Circle the answer.) b. The graph of f ( x) has no concavity/ one concavity/ two concavities (Circle the answer.) c. Write the equation(s) of any and all horizontal asymptotes to f ( x ), correct to three decimal places. d. Find f ( 0.5) = Round the answer correctly to three decimal places. e. Find x= when f ( x ) = 100. Round the answer correctly to three decimal places. ( / 6 pts ) 3. The endangered Macaya breast-spot frog lives in very high elevations and is one of the smallest frogs in the world. An estimate of its population is given by p( t ) = 1.67(0.851 t ) thousand frogs, where t is the number of years since 2007, 0 t 10. Checkpoint: p (2) = 1.2094 a. Find p( t) when t= 3. b. Write a sentence of interpretation for the answer to part (a) c. According to the model, in what year did the population drop to 0.5 thousand frogs? years after 2007 (Write the answer correctly rounded to three decimal places.) In what year would that occur? In ( / 7 pts ) Test continues on next page Page 10/12
4. The San Diego Zoo is the world s most visited zoo. In 2017, it charged 54 dollars per adult ticket and 44 dollars per child ticket. For 2017, A( x ) adult tickets gives the number of adult tickets sold on the th x day of January, 1 x 31. And C( x ) child tickets gives the number of child tickets sold on the x th day of January, 1 x 31. Use the information to complete the models. a. T ( x ) = January, 1 x 31. tickets gives the total number of tickets sold on the th x day of b. z( x ) = dollars gives the revenue from the sale of adult tickets and w( x ) = dollars gives the revenue from the sale of child tickets on the th x day of January, 1 x 31. c. R( x ) = dollars gives the total revenue from the sale of adult and child tickets on the th x day of January, 1 x 31. ( / 5pts ) 5. Choose exactly ONE of the following functions to answer each of the following. A function may be used in more than one blank. Do Not Abbreviate! LINEAR QUADRATIC CUBIC LOGARITHMIC EXPONENTIAL LOGISTIC Name one function that has: a. one concavity and one horizontal asymptote. b. one concavity and one vertical asymptote. c. a constant rate of change. d. a constant percentage change. e. two concavities and no asymptotes. ( / 5pts ) 6. 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 11/12
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 context 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 context 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 extra 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. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 12/12
Printed Name: Section #: Instructor: Please do not ask questions during this exam. 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 exam 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 Scantron Free Response Total Multiple Choice Total Total Possible Points 8 6 7 5 5 1 32 68 100 Points Earned Page 1/12
MULTIPLE CHOICE: 68 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. 1. [ 2 pts] Which one of the following options describes the graph? a. Concave up, increasing b. Concave down, decreasing c. Concave up, decreasing d. Concave down, increasing Answer the following two questions using the graph below. 2. On what interval(s) is the graph decreasing? a. (, 10 / 3 ),( 0,7 / 3) b. (, 1/ 3) c. (, 2) d. ( 2, 4 / 3) 3. Which one of the following is approximately the x-coordinate of an inflection point? 1 4 7 a. x = b. x = 2 c. x= d. x= 3 3 3 Page 2/12
4. Describe the end behavior of the following graph of f. a. lim f ( x) = 0 and lim f ( x) = 3 b. lim f ( x) = 3 and lim f ( x) = 0 x x x x c. lim f ( x) = and lim f ( x) = d. lim f ( x) = and lim f ( x) = x x x x Use the following graph of the function f ( x ) to answer the next three questions. 5. [2 pts] Find the limit: lim x 2 f ( x) =. a. 8 b. 3 c. -6 d. does not exist 6. [2 pts] Find the limit: lim x 2 + f ( x) = a. 8 b. 3 c. -6 d. does not exist 7. Which one of the following statements is true for the function f ( x )? a. f ( x) is continuous at x= 2. b. f ( x) is not continuous at x= 2 because f (2) is not defined. c. f ( x) is not continuous at x= 2 because lim f ( x) does not exist. x 2 d. The continuity of f ( x ) at x= 2 cannot be determined. Page 3/12
Use the following graph of the function f ( x ) to answer the next two questions. 8. Find the following limit: lim f ( x) =. x a. b. c. 2 d. -5 9. lim f ( x) = and this implies that ( ) x 2 f x has a vertical asymptote at. a., x= 2 b., x= 2 c., y= 2 d. 5, x = 5 10. A study of king penguins found a relationship between how deep the penguins dive to seek food and how long they stay under water. D( x) = 2.915x+ 0.015 yards gives the depth of a king penguin dive, where x is the duration of the dive in minutes, 1 x 9. Complete a sentence of interpretation for the slope of D( x ). When a king penguin dive is between 1 and 9 minutes,. a. the depth of the dive increases by 2.915 yards per minute that it remains underwater. b. the depth of the dive increases by 0.015 yards per minute that it remains underwater. c. the depth of the dive increases by 2.915 minutes per yard. d. the depth of the dive increases by 2.915 yards. Page 4/12
11. [2 pts] A relation is described in the table. Name an ordered pair that could be removed so that the remaining ordered pairs form a function, y as a function of x. a. ( 5,4 ) b. ( 1, 2) c. ( 4,7 ) d. ( 3,1 ) x 1 2 5 1 4 3 y 2 4 4-2 7 1 Use the following to answer the next two questions. The median weight of a female newborn, aged 0 months, is 7.0 pounds. Between 0 and 6 months of age, the median weight of a female infant increases by 1.5 pounds per month. 12. Complete the following model by filling in the blank. pounds gives the median weight of a female infant, t months since birth, 0 t 6. a. W( t ) = 7(1.015 t ) b. W ( t) = 1.5t+ 7 c. W( t ) = 7(1.5 t ) d. W ( t) = 7t+ 1.5 13. [2 pts] Fill in the blanks to the following sentence. Finding the median weight of a 5 month old girl with the above model uses and finding the weight of a 7 month old girl uses. a. interpolation; interpolation b. extrapolation; extrapolation c. extrapolation; interpolation d. interpolation; extrapolation 14. Albuterol is used to calm bronchospasm. It is typically inhaled in a 1.25 mg dose. The amount of albuterol left in the body decreases by 9.4 percent each hour. Find an equation to complete the model. mg gives the amount of albuterol left in the body x hours after an initial dose, 0 x 12. x x a. A( x= ) 1.25(0.906 ) b. A( x= ) 9.4(1.25 ) x c. A( x) = 9.4x + 1.25 d. A( x= ) 1.25(1.094 ) Page 5/12
Use the following to answer the next two questions. The population of a town in various years is given in the table below. Year 1990 1991 1992 1993 1994 Population, in thousands 5.093 6.871 9.278 12.542 16.917 15. Align the data to the number of years after 1990. A function that models the data, after the data was aligned to the number of years after 1990, is given. Complete the model for the aligned data. x P( x= ) 5.091(1.350 ). a. thousand people gives the population x years after 1990, 1990 x 1994. b. thousand people gives the population in year x, 1990 x 1994. c. thousand people gives the population x years between 1990 and 1994. d. thousand people gives the population x years after 1990, 0 x 4. 16. According to the model, which one of the following statements describes the constant percentage change in the town s population? Between the years 1990 and 1994, the population of the town. a. is increasing by 1.35% per year b. is increasing by 5.09% per year. c. is increasing by 35% per year d. is increasing by 65% per year. 17. For the first quiz of the semester, an instructor figured out that the total time spent grading p student papers was t( p) = 2 p+ 3 minutes, where p represents the number of papers graded,1 p 30. How is this function represented? a. Numerically b. Algebraically c. Graphically d. Verbally Page 6/12
Use the following to answer the next two questions. A small beach-side resort hotel uses seasonal pricing for its rooms to remain competitive during the busy summer months. th P( t ) hundred dollars per room is the price for a room for one night during the t month, 1 t 12. For instance, January is t= 1. th N( t ) rooms is the average number of occupied rooms during the t month, 1 t 12. For instance, January is t= 1. 18. [2 pts] What is the hotel s revenue for one night in July? a. P(7) + N (7) b. P( N (7)) c. P(7) N(7) d. N ( P (7)) 19. [2 pts] What are the units for the function that gives the hotel s revenue for one night in July? a. hundred rooms b. dollars c. dollars per room d. hundred dollars Use the following to answer the next two questions. Jennifer is training for a marathon that takes place in six months. h( x ) hours gives the cumulative amount of time Jennifer spends running, x weeks since the start of training for the marathon, 0 x 26. C( h ) calories is the number of calories burned while running for h hours, 0 h 125. 20. [2 pts] How can the two functions be combined to make a meaningful new function? a. multiplication, C( h) h( x) b. composition, C( h( x )) c. division, C( h) / h( x ) d. composition, h( C( x )) 21. [2 pts] What units will the new function have? a. hours b. calories c. calories per week d. calories per hour Page 7/12
22. P( t ) million dollars gives a company s profits t years since 2000 while C( t ) million dollars gives the company s total costs t years since 2000. Which one of the following equations has a solution that gives the break-even point? a. P( t ) = 0 b. P( t) = C( t) c. C( t ) = 0 d. P( t) = t 23. Find the linear function that is an inverse to W( L) using the nasal measurements of a gray kangaroo presented in the table below. L, Nasal Length (mm) 609 620 629 W, Nasal Width (mm) 222 233 241 L( W ) = mm is the nasal length of a gray kangaroo when W is its nasal width, 222 W 241 a. L( W ) = 701.013 + 242.436 ln( W ) b. L( W ) = 0.942L + 815.326 c. L( W) = 1.049W+ 375.861 d. L( W ) = 375.861W 1.049 24. Which of the following statements is TRUE concerning the graph of 3 2 f ( x) = 2x 4x 8? a. lim f ( x) = and lim f ( x) = b. lim f ( x) = and lim f ( x) = x x x x c. lim f ( x) = and lim f ( x) = d. lim f ( x) = and lim f ( x) = x x x x 25. Which of the following statements is TRUE concerning the graph of 2 f ( x) = 3x + 6x 10? a. It achieves a minimum value. b. It achieves a maximum value. c. It has two concavities. d. lim f ( x) = and lim f ( x) = x x Page 8/12
26. [2 pts] Which one of the following limits is suggested by the table? a. b. lim f ( x) = - x 1 x 1 lim f ( x) = - + c. lim f ( x) = 1 x d. lim f ( x) = -1 x x f ( x ) 0.9-15.100 0.99-195.000 0.999-1995.000 0.9999-19,995.000 0.99999-199,995.000 FREE RESPONSE: 32 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. The table below shows cumulative box office revenues on various days after the June 4, 2004 release of the movie: Harry Potter and the Prisoner of Azkaban. Days after release,t Cumulative Box Office revenues, R, in thousand dollars 1 5 16 30 50 80 38.268 109.363 185.308 221.403 240.500 246.901 a. Look at scatterplot of the data. How many concavities does it show? (Circle the answer.) no concavity/ one concavity/ two concavities b. Find a logarithmic function to model the data and write a completely defined model. ( /8pts) Page 9/12
157.345 2. Consider the following function: f ( x) = 1.895 1 + 12.275e x Checkpoint: f (2) = 123.17974 a. The graph of f ( x) is increasing/ decreasing (Circle the answer.) b. The graph of f ( x) has no concavity/ one concavity/ two concavities (Circle the answer.) c. Write the equation(s) of any and all horizontal asymptotes to f ( x ), correct to three decimal places. d. Find f ( 0.5) = Round the answer correctly to three decimal places. e. Find x= when f ( x ) = 100. Round the answer correctly to three decimal places. ( / 6 pts ) 3. The endangered Macaya breast-spot frog lives in very high elevations and is one of the smallest frogs in the world. An estimate of its population is given by p( t ) = 1.67(0.851 t ) thousand frogs, where t is the number of years since 2007, 0 t 10. Checkpoint: p (2) = 1.2094 a. Find p( t) when t= 3. b. Write a sentence of interpretation for the answer to part (a) c. According to the model, in what year did the population drop to 0.5 thousand frogs? years after 2007 (Write the answer correctly rounded to three decimal places.) In what year would that occur? In ( / 7 pts ) Test continues on next page Page 10/12
4. The San Diego Zoo is the world s most visited zoo. In 2017, it charged 54 dollars per adult ticket and 44 dollars per child ticket. For 2017, A( x ) adult tickets gives the number of adult tickets sold on the th x day of January, 1 x 31. And C( x ) child tickets gives the number of child tickets sold on the x th day of January, 1 x 31. Use the information to complete the models. a. T ( x ) = January, 1 x 31. tickets gives the total number of tickets sold on the th x day of b. z( x ) = dollars gives the revenue from the sale of adult tickets and w( x ) = dollars gives the revenue from the sale of child tickets on the th x day of January, 1 x 31. c. R( x ) = dollars gives the total revenue from the sale of adult and child tickets on the th x day of January, 1 x 31. ( / 5pts ) 5. Choose exactly ONE of the following functions to answer each of the following. A function may be used in more than one blank. Do Not Abbreviate! LINEAR QUADRATIC CUBIC LOGARITHMIC EXPONENTIAL LOGISTIC Name one function that has: a. one concavity and one horizontal asymptote. b. one concavity and one vertical asymptote. c. a constant rate of change. d. a constant percentage change. e. two concavities and no asymptotes. ( / 5pts ) 6. 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 11/12
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 context 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 context 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 extra 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. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 12/12