MATH 1020 TEST 1 VERSION A FALL 2018

Transcription

1 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. Use the following information to answer the net three questions. s( t) t billion dollars gives the amount of student debt in the US, t years since 2004, 0 t For the model above, state the input description ; and input units of measure. a. billion dollars; years b. number of years since 2004; years c. years; billion dollars d. amount of student debt in the US; billion dollars 2. Use the above model to complete the following sentence of interpretation for the slope: Between 2004 and 2016, the amount of student debt in the US increased by. a billion dollars per year b billion dollars c billion dollars per year d billion dollars 3. Write the following using function notation: In 2014, the amount of student debt in the US was 1, billion dollars. a. s(14) 1,142, 269,000,000 b. s(14) 1, c. s(10) 1, d. s(10) 1,142,269,000, In 1995, the population of Russia was million people. Between 1995 and 2005, Russia s population decreased by 0.5 percent each year. Use the given information to complete the model: R( ) million people gives the population of Russia, years since 1995, a b (0.995 ) c (1.005 ) d Page 3/11

2 5. The birth rate in Japan can be modeled by J( ) births for every thousand people, years after 1970, The constant percentage change for J( ) is. a % b. 97.6% c % d. -2.4% 6. The table below shows craft beer production in the US for various years. Align the input data to the number of years after Using the scatter plot, find the best fitting function to model the aligned data and write a completely defined model. Year Number of barrels, in millions a. B( ) 2.690(1.092 ) million barrels gives the yearly craft beer production in the US, years after 1994, b. c. d. 3 2 B( ) , ,950, million barrels gives the yearly craft beer production in the US, in year, B( ) million barrels gives the yearly craft beer production in the US, years after 1994, B( ) 6.854(10 )(1.092 ) million barrels gives the yearly craft beer production in the US, in year, R( ) million people gives the number of refugees worldwide, in year, S( ) million people gives the number of refugees who are from Syria, in year, Find a meaningful new function p( ) that describes the percentage of the total number of refugees worldwide who are from Syria in year. a. R( ) S( ) p( ) b. 100 S( ) p( ) 100 R( ) c. R( ) S( ) p( ) d. p( ) 100 R( S( )) 100 Page 4/11

3 Use the following information to answer the net two questions. [2 pts each] s( t ) thousand dollars gives the average student debt of a graduating college senior in the US, t years since h( s) months is the average amount of time it takes to pay off an average student debt of s thousand dollars. 8. Find a new meaningful function that can be constructed from the given models. a. s( t) h( s) b. h( s( t )) c. h( s) s( t) d. s( h( t )) 9. The new meaningful function constructed from the given models has input units and output units. a. thousand dollars, years per month b. years, thousand dollars per year c. thousand dollars, months d. years, months Use the following information to answer the net two questions. [2 pts each] An automobile dealership sells N( ) hundred Toyota Scion cars yearly when the price of its base model is thousand dollars per car, What is the dealership s yearly revenue R( ) from the sale of the Toyota Scion base model? a. R( ) N( ) b. R( ) N( ) c. R( ) d. R( ) N( ) 11. What are the output units for the yearly revenue R( ) from the sale of the Toyota Scion base model? a. thousand dollars per car b. thousand dollars c. hundred thousand dollars d. hundred cars per thousand dollars Page 5/11

4 12. When interchanging the input and output values of an eponential growth function, the resulting inverse function is. a. an eponential decay function b. logarithmic c. logistic d. cubic 13. Which one of the following its is suggested by the table? a. g( ) = 0 0 b. g( ) = c. g( ) = - 0 d. g( ) = 0 g( ) , , , A student club is planning a fund raiser formal dinner-dance. The club has projected the following total costs and revenue. C( ) dollars is the cost associated with the production of the formal dinner- dance, when tickets are sold, R( ) 50 dollars is the revenue from the sale of tickets to the formal dinner-dance, How many tickets must be sold so that the student club will break-even? a. 20 b. 30 c. 50 d. 100 Page 6/11

5 Use the following graph of the function f ( ) to answer the net five questions. [2 pts each] a. 5 b. 5 c. d. 16. a. 5 b. 5 c. d. 17. The equation of the horizontal asymptote to the graph of f ( ) is. a. 1 b. 5 c. y 5 d. y The graph of f ( ) is increasing on the interval(s). a. (,1) only b. (1, ) only c. (,1) and (1, ) d. nowhere 19. The graph of f ( ) is concave up on the interval(s). a. (,1) only b. (1, ) only c. (,1) and (1, ) d. nowhere Page 7/11

6 20. Complete the following for the function f ( ) ln( ). and f ( ). a. ; has two asymptotes b. zero; has two asymptotes c. ; has one asymptote d. zero; has one asymptote Which one of the following statements regarding the function f ( ) e is FALSE? a. y is a horizontal asymptote. b. f ( ) c. The function is decreasing. d. y 0 is a horizontal asymptote. 22. Which one of the following functions has a graph with f ( )? a. f ( ) a(2 ), a 5 b. c. f ( ) a b, a 3 d. 2 f ( ) a b c, a f ( ) a b c d, a [2 pts] Which one of the following relations does NOT satisfy the definition of a function, given is the input variable and y is the output variable? 1 y b. y 5 1 c. a e y 2 d The graphs below are two eamples of a(n) function. a. logarithmic b. eponential c. quadratic d. logistic Page 8/11

7 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 S( ) million people gives the number of registered Skype users, years since (the end of) 2004, 0 3. Checkpoint: S( 3) a. Find S( ) when 2. Write a sentence of interpretation. b. Part (a) uses interpolation/ etrapolation (circle one). c. Use the model to complete the following sentence: If the trend indicated by the model continued, the number of Skype users was projected to reach 428,000,000 people years after (the end of) 2004, in the year. (round answer to 3 decimal places) (specify the year) / 9pts 2. In each of the following, circle all function types having a. eactly one concavity. linear eponential logarithmic logistic quadratic cubic b. eactly one inflection point. linear eponential logarithmic logistic quadratic cubic c. no concavity. linear eponential logarithmic logistic quadratic cubic d. a constant percentage change. linear eponential logarithmic logistic quadratic cubic / 7pts Page 9/11

8 3. Use the graph of function f ( ) below to answer the following questions. a. Fill in the blanks. A it must specify a number,,, or DNE (if the answer does not eist or is undefined) _ f (2) b. Which one of the four statements below is TRUE? Circle the correct sentence. The function f ( ) is continuous at 2. The function f ( ) is not continuous at 2 because f (2) The function f ( ) is not continuous at 2 because 2 is undefined. f ( ) does not eist. The function f ( ) is not continuous at 2 because f (2) f ( ). 2 c. Fill in the blanks. A it must specify a number L,,, or DNE (if the answer does not eist or is undefined). d. Consider the portion of the graph of f ( ) on the interval 2 2. How many inflection points are there? Circle the answer. Zero inflection points on 2 2 One inflection point on 2 2 Two inflection points on 2 2 Three inflection points on 2 2 / 9pts Page 10/11

9 4. For a ride with UberSelect in Los Angeles, Uber charges a flat fee of $5.00 and $2.35 for each mile traveled. Find an equation that completes the model: U( ) dollars gives the fare for a ride of miles with UberSelect in Los Angeles, 0. / 3pts 5. A band called The Chainsmokers released a single called #selfie on January 29, The table below shows the total number of downloads, in thousands, of the single #selfie for various weeks since the single was released. Weeks since release Number of Downloads, in thousands a. Look at scatter plot of the data. How many concavities are suggested by the scatter plot of the data? Circle one: b. Find a logistic function to model the data and write a completely defined model. / 9pts 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 11/11