MATCH Problems 29 Through 38 with the Appropriate Model

PRACTICE TEST – FUNCTIONS SPRING 2012

MATCH problems 29 through 38 with the appropriate model.

A. absolute value model D. logarithmic model B. exponential model E. quadratic model C. linear model F. rational model

29. y = 6x - 45 30. Finds maximum or 5 31. y  minimum x  2

32. Describes population growth 33. y = 6x2 - 5x + 10 34. y = 1000(1.05)x

35. 36. 37. 38.

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.

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:

Type of function: ______

Regression equation: ______

Correlation coefficient: ______

Good fit? _____ Why/why not?

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:

A. Identify the independent variable:

B. Identify the dependent variable:

C. The ordered pairs would be:

D. Identify the constant rate of change:

E. Identify the initial value:

F. The linear model for this problem is ______.

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:

A. Identify the independent variable:

B. Identify the dependent variable:

C. The ordered pairs would be:

D. Identify the constant rate of change:

F. The linear model for this problem is ______.

G. The value of the machine after 8 years would be ______.

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.]

A. Identify the independent variable.

B. Identify the dependent variable.

C. Complete the table to show the population of the city each year from 1990 to 2000.

Year 1990 '91 '92 '93 '94 '95 '96 '97 '98 '99 2000 Time 0 Pop.

D. Graph the data.

F. Identify the rate of change:

G. The equation for this problem is:

H. The population in 2025 would be: PRACTICE TEST – FUNCTIONS KEY

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.

41. A. # bks, thousands X = # of books ordered, in thousands B. $ price per book Y

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.

41. A. X = time in years

B. Y = value of machine, $

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.

F. Y = - 5000x + Y = (constant rate of change) X + (initial value) 60,000 G. $20,000 Substitute 8 for x and find y.

42. A. X = time, in years Time since 1990, the beginning

B. Y = population

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.]

H. 1,182,828 Substitute 35 years (2025 – 1990) for x and find y.