<p>PRACTICE TEST – FUNCTIONS SPRING 2012</p><p>MATCH problems 29 through 38 with the appropriate model.</p><p>A. absolute value model D. logarithmic model B. exponential model E. quadratic model C. linear model F. rational model</p><p>29. y = 6x - 45 30. Finds maximum or 5 31. y  minimum x  2</p><p>32. Describes population growth 33. y = 6x2 - 5x + 10 34. y = 1000(1.05)x</p><p>35. 36. 37. 38.</p><p>39. Indicate the WINDOW settings to graph the following ordered pairs in a SCATTER PLOT. Be sure your graph makes maximum use of the window. Sketch the graph below.</p><p>Ordered pairs (-3, 0.13) (-2, 0.28) (-1, 0.5) (0, 1) (1, 2) (2,5) (4,15) WINDOW Xmin: Xmax: Xscl: Ymin: Ymax: Yscl:</p><p>Type of function: ______</p><p>Regression equation: ______</p><p>Correlation coefficient: ______</p><p>Good fit? _____ Why/why not?</p><p>40. The setup fee for a math textbook is $50. The price per book depends on the number of thousands of the textbook ordered. If 20,000 are ordered, the price per book is $38. The price per book is $26 if 40,000 are ordered. Answer the following:</p><p>A. Identify the independent variable:</p><p>B. Identify the dependent variable:</p><p>C. The ordered pairs would be:</p><p>D. Identify the constant rate of change:</p><p>E. Identify the initial value:</p><p>F. The linear model for this problem is ______.</p><p>G. How much would the textbook cost if 25,000 books were ordered? 41. For tax purposes, a machine is depreciated linearly over a 12-year period. Thus, at the end of 12 years, the machine is considered to have no value. Assuming that the original machine cost $60,000, answer the following:</p><p>A. Identify the independent variable:</p><p>B. Identify the dependent variable:</p><p>C. The ordered pairs would be: </p><p>D. Identify the constant rate of change:</p><p>E. Identify the initial value:</p><p>F. The linear model for this problem is ______.</p><p>G. The value of the machine after 8 years would be ______.</p><p>42. In 1990, the population of a certain city was 80,000, and it has been growing at a steady rate of 8% per year since then. [HINT: See notes from M&M team task.]</p><p>A. Identify the independent variable.</p><p>B. Identify the dependent variable.</p><p>C. Complete the table to show the population of the city each year from 1990 to 2000. </p><p>Year 1990 '91 '92 '93 '94 '95 '96 '97 '98 '99 2000 Time 0 Pop.</p><p>D. Graph the data.</p><p>E. Identify the initial value:</p><p>F. Identify the rate of change:</p><p>G. The equation for this problem is: </p><p>H. The population in 2025 would be: PRACTICE TEST – FUNCTIONS KEY</p><p>29. - 38. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. C E F B E B E C A D 40. Exponential; y = 1.05 ( 1.99)x ; r = 0.998; yes, very good fit because it is close to 1.</p><p>41. A. # bks, thousands X = # of books ordered, in thousands B. $ price per book Y</p><p>C. (# bks, price) (20, 38) and (40, 26) The last three zeros (thousands) may be dropped for ordered pairs as long as the same number of zeros are dropped. D. Slope = y y2  y1 26  38 12  3  3      0.6  0.6 x x2  x1 40  20 20 5 5 E. 50 Initial value = y-intercept = 50. This is the ordered pair (0, 50)  For 0 books ordered, there is a set-up fee of $50. F. y = -0.6 x + 50 Dependent variable = constant rate of change X independent variable + initial value G. $35 Substitute 25 for x and solve for y.</p><p>41. A. X = time in years</p><p>B. Y = value of machine, $</p><p>C. (yrs, $) (0, 60,000) for the beginning value and (12, 0) “at the end of 12 years there is no value” D. - 5000 y  y 0  60,000  60,000 2 1    5000 x2  x1 12  0 12 E. 60,000 At time = 0 (brand new), the value is 60,000.</p><p>F. Y = - 5000x + Y = (constant rate of change) X + (initial value) 60,000 G. $20,000 Substitute 8 for x and find y.</p><p>42. A. X = time, in years Time since 1990, the beginning</p><p>B. Y = population</p><p>C. (0, 80,000) (1, 86,4000), (2, 93,312), (3, 100,777), (4, 108,839), (5, 117,546), (6, 126,450), (7, 137,106), (7, 148,074), (8, 159,920), (9, 172,714) D. E. 80,000 F. 8% G. y = 80,000 (1 + .08)x [ exponential bc % change -> dependent variable = initial value (1 + rate)time It is + this time because it is growing; minus would be decreasing or decay.]</p><p>H. 1,182,828 Substitute 35 years (2025 – 1990) for x and find y.</p>