Math 1020 ANSWER KEY TEST 3 VERSION B Fall 2018

Transcription

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 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 while the student is in the testing room. The only calculators to be used are TI-8, TI-8+, TI-84 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.) General Directions and Calculator Hints are located on the last page. FR# FR # FR # FR#4 scantron Free Response Total Multiple Choice Total Total Possible points Points Earned Formula: f () = f() c + f ()( c c ) L Page of

2 MULTIPLE CHOICE: 6 points Use a # 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.) Each question is worth points, unless noted otherwise. There is no penalty for guessing on multiple choice questions. If you indicate more than one answer, or you leave a blank, the question will be marked as incorrect. D A B A C A B D C B B A A B C D D C B A D C B D C. For f( ) = ln( ) +, find f ( ) =. a. + b. + ln( ) c. + d. +. For g= ( ) 4( ), find g ( ) =. a. 4ln() b. ln() c. 4 ln() d. 4( ) + 4ln() e. If s ( ) =, find s ( ) =. 5 a. 5e b. e 5 c. e d. 5 5 ( e ) 5 e df 4. Find d = when ( ) 4 f = e. a. e b. 4 ( e ) c. 4 e d. e Page of

3 (5+ ) 5. [ pts] f( ) = e is a composition gh ( ( )) of two functions, gh ( ) and h ( ). Identify the two functions. a. gh ( ) e, h ( ) e 5 = = b. gh ( ) e, h ( ) 5 = = + h c. gh ( ) = e, h ( ) = 5+ d. gh ( ) =, h ( ) = e (5+ ) 6. [ pts] gh ( ) = h and h ( ) = 7 can be combined as the composition g ( ) = gh ( ( )). What is dg d? a. ( 7 ) 7 ln() b. ( 7 ) c. ln() (7 ) + 7 d. 7ln() 7. [ pts] A farmer in Washington State sells honey from the honeybees she raises. She sells hp ( ) hundred pounds of honey when the price is set at p dollars per pound,.99 p Find a function that describes the revenue from the sale of honey and then complete the following statement. When the price of honey is p dollars per pound, the revenue from the sale of honey is changing by hundred dollars per dollar per pound. a. php ( ) b. hp ( ) + ph ( p) c. h ( p) d. p h ( p) 8. [ pts] Use the following information to find the derivative f () = if g ( ) and h ( ) can be combined as f( ) = g ( ) h ( ). g () = 9, h () = 5, g () = 0.8, h () =.5 a.. b.. c. 0. d. 9.5 Page of

4 Use the information below to answer the following three questions. [ pts each] v ( ) million visitors gives the number of people to visit Charleston, SC, years after 000. cv () billion dollars gives the economic impact of v million visitors to Charleston, SC. In 06, there were 5.06 million visitors to Charleston, SC and that number was increasing by.794 million visitors per year. When there were 5.06 million visitors, the economic impact to Charleston, SC was 4. billion dollars and that number was increasing by.756 billion dollars per million visitors. A new meaningful function cv ( ( )) can be constructed using the two functions v ( ) and cv (). 9. The economic impact to Charleston, SC in 06 was billion dollars. a b..547 c. 4. d In 06, how quickly was the economic impact to Charleston, SC changing with respect to time? Give the numeric answer here and the output units in the net question. a b..50 c..756 d The units to the previous question are: a. billion dollars per million visitors b. billion dollars per year c. billion dollars d. trillion dollars per year. For f( ) = ( + ) +, find f ( ) =. ( ) ( ) ( + ) + ( + ) + + a. ( ) ( + ) + + ( + ) + b. ( ) c. ( ) d. ( ) Page 4 of

5 Use the following information to answer the net four questions. The slope graph below gives the RATE OF CHANGE in the national average price of gasoline in the US, m months since (the end of) December 0, m 4.. On the given interval, the national average price of gasoline in the US was at a relative maimum month(s) after the end of 0. a. 4.9 b. 9 c. d. never 4. On the given interval, the national average price of gasoline in the US was at an inflection point month(s) after the end of December 0. a. 4.9 b. 9 c. d. never 5. On the given interval, the national average price of gasoline in the US was decreasing between months after the end of December 0. a. and 9 only b. and 4.9 only c. 4.9 and only d. and 4.9, and 4 6. [ pts] What are the output units for the second derivative G ( m)? a. dollars/gallon b. dollars/gallon per month per gallon c. dollars/gallon per month d. dollars/gallon per month per month 7. For a differentiable function g, solutions to the equation g ( ) = 0 indicate the location of and solutions to the equation g ( ) = 0 indicate the location of. a. the zeros of g ; possible inflection points of g b. possible inflection points of g ; possible relative etreme points of g c. possible relative etreme points of g ; zeros of g d. possible relative etreme points of g ; possible inflection points of g Page 5 of

6 8. The graph of function f is shown below. Identify the graph of its second derivative f. a. b. c. d. Use the graph below to answer the following two questions. [ pts each] The graph of the second derivative function f for a differentiable function f is shown below. Answer the following questions about the function f on the given interval (0,5). 9. According to the graph of its second derivative, the inflection point(s) on function f( ) occur(s). a. nowhere b. at =.55 c. at = 4. d. at =. and = According to the graph of its second derivative, f( ) is concave up on the interval. a. (.55, 5) b. (0,.) and (5.5, 5) c. (0,.55) d. (0, 4.) Page 6 of

7 Answer the following three questions about the function f graphed below. [ pts each]. On the closed interval [ 5.9,6], an absolute maimum occurs at. a. = 5.9 b. = 0.75 c. =.5 d. = 6. On the closed interval [ 5.9,6], there is/are relative etrema points. a. one b. two c. three d. five. On the open interval ( 5.9,6), there is/are inflection points. a. one b. two c. three d. four 4. In Clemson, on August, there were hours and 55 minutes of daylight, and the number of daylight hours was decreasing by hour and minutes per month. The number of daylight hours in Clemson in mid-september was approimately. a. hours and 6 minutes b. hours and 8 minutes c. hours 5 minutes d. hours and 4 minutes Page 7 of

8 5. What is the linearization for a function f at input c = 5, if f (5) = and f (5) =.45? a. f ( ) = ( 0.689) b. f ( ) = (.45) L c. f ( ) = ( 5) d. f ( ) = ( 5) L L L FREE RESPONSE: 8 points Show work where possible. Read the directions on rounding, inclusion of units, and writing models and sentences at the back of the test.. S ( ) gives the total number of states to legally require the use of seatbelts, years after highway funds were tied to such legislation by the US federal government, 0 8. Also, S (7) = 4 and S (7) =. Use the given information and the graph of S ( ) to answer the questions below. Part a:.5 points Part b:.5 points a. Use the given information to estimate the total number of states that legally required the use of seatbelts eight years after highway funds were tied to such legislation by the US federal government. Show work. S(8) S(7) + S (7) = 4 + = states Since the tangent line lies below the curve at = 7, the estimate is an underestimate Is this an underestimate or overestimate (circle one)? b. Use the information to estimate the total number of states that legally required the use of seatbelts si years after highway funds were tied to such legislation by the US federal government. Show work. S(6) S(7) + ( ) S (7) = 4 = 9 9 states Since the tangent line lies below the curve at = 7, the estimate is an underestimate. Is this an underestimate or overestimate (circle one)? ( / 5 pts ) Page 8 of

9 . c ( ) thousand students gives Clemson University s student enrollment, years after 000, 0 5. a ( ) gives the proportion of Clemson University students in the College of Architecture, Arts & Humanities (College of AA&H), years after 000, 0 5. (Eample: a () = means 9.0 %) Given: c () =.0, a () = 0.090, dc = 0.554, d = da = d = a. The two functions c ( ) and a ( ) can be used to construct a new meaningful function s ( ) using: Part a: points Part b: points Part c: points Part d: points function composition / function multiplication _(Circle one) b. In 0, how many students were enrolled in the College of AA&H? Show work, with the answer correctly rounded to three decimal places. Include units with the answer. c() a() = (.0)(0.090) =.97 thousand students (enrolled in the College of AA&H) c. ds Find = d = Show work, with the answer correctly rounded to three decimal places. ds = c () a() + c() a () = (0.554)(0.090) + (.0)( 0.006) = d = d. Interpret the answer to part c) by filling in the blanks in the sentence below. In 00, the number of students enrolled in the College of AA&H was (what)) decreasing by thousand students per year. (number and units) ( /0 pts ) Page 9 of

10 . Find the derivative of the following functions. Use eact numbers. It is not necessary to simplify. Any work shown and the final answer should be clearly presented with proper notation. 7 a. f( ) = 4 + Part a: 5.5 pts Part b: 4.5 pts 7 f( ) = = ( )( ) ( ) ( ) ( ) ( ) ( )( ) f ( ) = ( ) 4 + (8+ ) = (8+ ) b. g ( ) = ln(6 + ) g ( ) = ( /0 pts ) TEST CONTINUES ON NEXT PAGE Page 0 of

11 4. 5 D ( ) = 7.85( 0 ) million people gives the population of the Detroit Metropolitan area, years after 960, Check point: D () = Note: Please notice that the coefficient of the first term includes 5 0. Part a: 4 points Part b: 4 points Part c: 4 points a. Fill in the blanks, correctly rounded to three decimal places. Answers that are not rounded correctly to three decimal places will be marked wrong. Between 960 and 000, the population of the Detroit Metropolitan area was decreasing most rapidly.7 years after 960, at which time the population was decreasing by 0.00 million people per year. At that time, the Detroit Metropolitan area had a population of 4.64 million people. b. Identify the following, correctly rounded to three decimal places. Answers that are not rounded correctly to three decimal places will be marked wrong. Find the relative etrema in the Detroit Metropolitan area s population, on the interval Relative minimum: =.706 and y = 4.4 Relative maimum: =.58 and y = _ c. Identify the absolute etrema on the interval 0 40 to fill in the blanks in the following sentences. Answers that are not rounded correctly to three decimal places will be marked wrong. Between 960 and 000, the population of the Detroit Metropolitan area was lowest 0 years after 960 and at that time, the population was 4.06 million people. Between 960 and 000, the population of the Detroit Metropolitan area was highest _.58 years after 960 and at that time, the population was million people. ( / pts ) point for correctly filling out and bubbling the scantron with a # pencil, a correct XID, a correct test version AND the front of the test is completed with your signature on the academic integrity statement. END OF TEST Page of

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. Round your answers to 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 less than decimal places. When you are 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 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 L, L, etc., you may reinsert them using STAT 5 (set-up editor) enter. The SCATTER PLOT will not show unless Plot has been turned on and there is data in L and L. ZOOM 0 may not work for graphing if Plot is turned on. DIM MISMATCH error usually means that the lists in L and L are not of equal length. DATA TYPE error usually means that you already have something in Y 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 Y. If you need to CLEAR MEMORY, use nd +, 7:Reset, :All Ram, :Reset Page of