Answer Key_Test 1_Version A_Spring 2018

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 1/12 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 Scan- tron Free Response Total Multiple Choice Total Total Possible Points 8 6 7 5 5 1 32 68 100 Points Earned

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 2/12 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? a. 1 3 x = - b. 2 x = - c. 4 3 x = d. 7 3 x = _________________________________________________________________________________________ MC: C D A B A| C C D A A| B B D A D| C B C D B| B A C C B| A

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 4/12 _________________________________________________________________________________________ Use the following graph of the function ( ) f x to answer the next two questions. 8. Find the following limit: lim ( ) _______________ x f x →∞ = . a. ∞ b. -∞ c. 2 d. -5 9. 2 lim ( ) __________ x f x - → = and this implies that ( ) f x has a vertical asymptote at ________________. a. -∞ , 2 x = b. ∞ , 2 x = c. -∞ , 2 y = d. 5 - , 5 x = - _________________________________________________________________________________________ 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. ( ) 2.915 0.015 D x x = + yards gives the depth of a king penguin dive, where x is the duration of the dive in minutes, 1 9 x ≤ ≤ . 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.

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 5/12 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 _________________________________________________________________________________________ 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 6 t ≤≤ . a. ( ) 7(1.015 ) t W t = b. ( ) 1.5 7 W t t = + c. ( ) 7(1.5 ) t W t = d. ( ) 7 1.5 W t t = + 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 12 x ≤ ≤ . a . ( ) 1.25(0.906 ) x A x = b. ( ) 9.4(1.25 ) x A x = c. ( ) 9.4 1.25 A x x = - + d. ( ) 1.25(1.094 ) x A x = x 1 2 5 1 4 3 y 2 4 4 -2 7 1

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 7/12 _________________________________________________________________________________________ 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. ( ) P t hundred dollars per room is the price for a room for one night during the th t month, 1 12 t ≤ ≤ . For instance, January is 1. t = ( ) N t rooms is the average number of occupied rooms during the th t month, 1 12 t ≤ ≤ . For instance, January is 1. t = 18. [2 pts] What is the hotel’s revenue for one night in July? a. (7) (7) P N + b. ( (7)) P N c. (7) (7) P N ⋅ d. ( (7)) N P 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 26 x ≤ ≤ . ( ) C h calories is the number of calories burned while running for h hours, 0 125 h ≤ ≤ . 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 _________________________________________________________________________________________

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 8/12 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. ( ) 0 P t = b. ( ) ( ) P t C t = c. ( ) 0 C t = 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, 222 241 W ≤ ≤ a. ( ) 701.013 242.436ln( ) L W W = - + b. ( ) 0.942 815.326 L W L = - + c. ( ) 1.049 375.861 L W W = + d. ( ) 375.861 1.049 L W W = - 24. Which of the following statements is TRUE concerning the graph of 3 2 ( ) 2 4 8 f x x x = - - ? a. lim ( ) x f x → - ∞ = -∞ and lim ( ) x f x → ∞ = -∞ b. lim ( ) x f x → - ∞ = ∞ and lim ( ) x f x → ∞ = -∞ c. lim ( ) x f x → - ∞ = -∞ and lim ( ) x f x → ∞ = ∞ d. lim ( ) x f x → - ∞ = ∞ and lim ( ) x f x → ∞ = ∞ 25. Which of the following statements is TRUE concerning the graph of 2 ( ) 3 6 10 f x x x = - + - ? a. It achieves a minimum value. b. It achieves a maximum value. c. It has two concavities. d. lim ( ) x f x →-∞ = ∞ and lim ( ) x f x →∞ = ∞

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 10/12 2. Consider the following function: 1.895 157.345 ( ) 1 12.275 x f x e - = + Checkpoint: (2) 123.17974 f = 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. 0 y = and 157.345 y = d. Find ( 0.5) _ 4.8 _ __ 18 f - = Round the answer correctly to three decimal places. e. Find 1.6 _ __ 17 x = when ( ) 100 f x = . Round the answer correctly to three decimal places. ( ) 100 1.617 f x x = = ( ) _______ / 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 ( ) 1.67(0.851 ) t p t = thousand frogs, where t is the number of years since 2007, 0 10 t ≤≤ . Checkpoint: (2) 1.2094 p = a. Find ( ) p t when 3 t = . (3) 1.029 p = b. Write a sentence of interpretation for the answer to part (a) In 2010, the population of Macaya breast-spot frogs was 1.029 thousand frogs. c. According to the model, in what year did the population drop to 0.5 thousand frogs? ( ) 0.5 7.475 p t t = = __________ 7.475 __________ years after 2007 (Write the answer correctly rounded to three decimal places.) In what year would that occur? In __ 2015 _____ ( ) _______ / 7 pts Test continues on next page Part a) 1 pt Part b) 1 pt Part c) 2 pts Part d) 1 pt Part e) 1 pt Part a) 2 pts Part b) 3 pts Part c) 2 pts

MATH 1020 ANSWER KEY TEST 1 VERSION A SPRING 2018 Page 11/12 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 31. x ≤ ≤ And ( ) C x child tickets gives the number of child tickets sold on the th x day of January, 1 31. x ≤ ≤ Use the information to complete the models. a. ( ) ___ ( _ ( ) __ ) _ A x C x T x + = tickets gives the total number of tickets sold on the th x day of January, 1 31. x ≤ ≤ b. 5 ( ) ____ ____ _ ( _ 4 ) __ A x z x = dollars gives the revenue from the sale of adult tickets and 44 ( ) _____ _ ___ ( _ ) _ C x w x = dollars gives the revenue from the sale of child tickets on the th x day of January, 1 31. x ≤ ≤ c. ( ) ( ) or ( ) __ _ 54 ___ ( ) 44 ( ) z x w x A C x x x R + = + dollars gives the total revenue from the sale of adult and child tickets on the th x day of January, 1 31. x ≤ ≤ ( ) _______ /5 pts 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. _______ Exponential _______________ b. one concavity and one vertical asymptote. _______ Logarithmic _______________ c. a constant rate of change. ________ Linear ___________________ d. a constant percentage change. _______ Exponential ______________ e. two concavities and no asymptotes. ________ Cubic _____________ ( ) _______ /5 pts 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 Parts a-e, 1 pt per blank Part a) 2 pts Part b) 2 pts Part c) 1 pt