Deck 1: Functions and Applications

Question 1

Find the best-fit line associated with the set of points. $( 1,5 )$ , $( 3,14 )$ , $( 5,24 )$ , $( 7,0 )$

A) $y = 2.0 x + 2.8$
B) $y = - 0.3 x - 11.8$
C) $y = 2.0 x + 11.8$
D) $y = - 0.3 x + 11.8$
E) $y = x - 11.8$

Answer 1

$y = - 0.3 x + 11.8$

Question 2

The chart shows second quarter total retail e-commerce sales in the U.S. in 1999, 2001 and 2003 ( $t = 0$ represents 1999). Find the regression line. Round coefficients to two decimal places. $$\begin{array} { | l | l | l | l | } \hline \text { Year } \boldsymbol { t } & 0 & 2 & 4 \\\hline \text { Sales (S Billion) } & 4 & 8 & 13 \\\hline\end{array}$$ Use the regression line to estimate second quarter retail e-commerce sales in 2000. Round your answer to two decimal places.

A)$3.04 billion
B) $18.24 billion
C) $12.16 billion
D) $6.08 billion
E) $6.69 billion

Answer 2

$6.08 billion

Question 3

Find the coefficient of correlation of the line that best fits the data set.
​ ​
Please give the answer to four decimal places if necessary.

Answer 3

1

Question 4

Use correlation coefficients to determine which of the given sets of data is worst fit by its associated regression line.
a) $\{ ( 2,6 ) , ( - 4,18 ) , ( 4,2 ) \}$
b) $\{ ( 0,1 ) , ( 1,0 ) , ( 2,1 ) \}$
c) $\{ ( 0,0 ) , ( 5 , - 5 ) , ( 2 , - 2.2 ) \}$

A)a
B) b and c
C) c
D) a and b
E) b

Question 5

In 2004 the Texas Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The table gives the approximate number of jobs for the citizens of Texas that would be created at various levels of recovery. Find the regression line. $$\begin{array} { | l | l | l | l | l | } \hline \text { Percent Recovery (\%) } - \boldsymbol { x } & 20 & 40 & 80 & 100 \\\hline \text { Jobs Created (Millions) } - \boldsymbol { y } & 3 & 6 & 9 & 15 \\\hline\end{array}$$ Use the regression line to estimate the number of jobs that would be created at a recovery level of 85%.

A) $y ( 85 ) = 10.525$ million jobs
B) $y ( 85 ) = 23.25$ million jobs
C) $y ( 85 ) = 12.625$ million jobs
D) $y ( 85 ) = 12.125$ million jobs
E) $y ( 85 ) = 11.625$ million jobs

Question 6

Find the coefficient of correlation of the line that best fits the data set.
​ ​
Please give the answer to four decimal places if necessary.

Question 7

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 2,10 ) , ( - 2 , - 12 ) , ( 7,44 ) \}$

A) $r = 0.9983$
B) $r = 0.4992$
C) $r = 0.6988$
D) $r = 0$
E) $r = 0.7986$

Question 8

Find the best-fit line associated with the set of points. $( 1,5 )$ , $( 2,10 )$ , $( 3,16 )$

A) $y = 5.5 x - 0.67$
B) $y = x$
C) $y = 5.5 x$
D) $y = 5.5 x + 0.67$
E) $y = 5.5 x - 1$

Question 9

Find the best-fit line associated with the set of points. $( 0,3 )$ , $( 1,4 )$ , $( 4,10 )$ , $( 5,14 )$

A) $y = 2.15 x - 2.38$
B) $y = x - 2.38$
C) $y = x + 2.38$
D) $y = 2.71 x + 0.96$
E) $y = 2.15 x + 2.38$

Question 10

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 0,0 ) , ( 4,15 ) , ( 7,18 ) \}$

A) $r = - 0.2879$
B) $r = 0.9596$
C) $r = 0.2879$
D) $r = - 0.9596$
E) $r = 0.6238$

Question 11

The table shows soybean production, in millions of tons, in Brazil's Cerrados region, as a function of the cultivated area, in millions of acres. Use technology to obtain the regression line. Round coefficients to two decimal places. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Area (Millions of Acres) } \boldsymbol { x } & 25 & 30 & 32 & 40 & 52 \\\hline \text { Production (Millions of Tons) } - \boldsymbol { y } & 14 & 25 & 30 & 40 & 60 \\\hline\end{array}$$

A) $y = 1.64 x - 24.94$
B) $y = 1.64 x + 24.94$
C) $y = 16.4 x + 24.94$
D) $y = - 1.64 x - 24.94$
E) $y = - 16.4 x + 24.94$

Question 12

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 5 , - 23 ) , ( - 2 , - 2 ) , ( 7 , - 29 ) \}$

A) $r = - 0.16$
B) $r = - 1$
C) $r = - 0.45$
D) $r = 0$
E) $r = 0.9999$

Question 13

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 0,8 ) , ( 2,8 ) , ( - 7,19 ) \}$

A) $r = 1$
B) $r = - 0.4887$
C) $r = - 0.6841$
D) $r = 0$
E) $r = - 0.9774$

Question 14

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 2,9 ) , ( 5,15 ) , ( 9,23 ) \}$

A) $r = 1$
B) $r = - 1$
C) $r = 0.6$
D) $r = - 0.2$
E) $r = 0.2$

Question 15

Find the regression line associated with the set of points. Round all coefficients to 4 decimal places. $( 1,1 )$ , $( 2,1 )$ , $( 4,2 )$

A) $y = 1.3571 x - 1$
B) $y = 0.3571 x - 1$
C) $y = 1.3571 x + 1$
D) $y = 0.2571 x$
E) $y = 0.3571 x + 1$

Question 16

Following are approximate values of the Amex Gold BUGS Index. $\begin{array} { | l | l | l | l | } \hline \text { Year } \boldsymbol { x } & 0 & 2 & 4 \\\hline \text { Index } \boldsymbol { y } & 50 & 100 & 250 \\\hline\end{array}$ ( $$x = 0$$ represents 2000)
Obtain the associated regression line. (Round coefficients to 2 decimal places if necessary.) Use your regression equation to project the 2001 sales.

A)65.33
B) 83.33
C) 93.33
D) 63.33
E) 94.33

Question 17

Find the best-fit line associated with the set of points. $( 0,3 )$ , $( 1,3 )$ , $( 2,6 )$

A) $y = 2.5 x - 1.5$
B) $y = 2.5 x + 1.5$
C) $y = 1.5 x + 2.5$
D) $y = x + 2.5$
E) $y = 1.5 x - 2.5$

Question 18

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 3,3 ) , ( 5,4 ) , ( 7,6 ) \}$

A) $r = 0.9820$
B) $r = - 0.9820$
C) $r = - 0.7856$
D) $r = 0.3641$
E) $r = 0.7856$

Question 19

Following are forecasts of worldwide annual cell phone handset sales. $$\begin{array} { | l | l | l | l | } \hline \text { Year } \boldsymbol { x } & 3 & 5 & 7 \\\hline \text { Sales } \boldsymbol { y } \text { (Millions) } & 500 & 600 & 800 \\\hline\end{array}$$ ( $$x = 3$$ represents 2003)
Obtain the associated regression line. (Round coefficients to 2 decimal places if necessary.) Use your regression equation to project the 2017 sales.

A)1533.33
B) 1523.33
C) 1543.33
D) 1547.33
E) 1516.33

Question 20

The table shows the number of fiber-optic cable connections to homes in the U.S. from 2000 to 2004 ( $t = 0$ represents 2000). Use technology to obtain the linear regression line, with regression coefficients rounded to two decimal places. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Year } t & 0 & 1 & 2 & 3 & 4 \\\hline \text { Connections } c \text { (Thousands) } & 0 & 10 & 25 & 65 & 150 \\\hline\end{array}$$

A) $c = 35.5 t - 21$
B) $c = - 35.5 t - 21$
C) $c = 35.5 t + 21$
D) $c = 142 t - 21$
E) $c = - 142 t + 21$

Question 21

The linear function is given. Find $$f ( 0 )$$ . $$\begin{array} { | l | l | l | l | l | } \hline \boldsymbol { x } & 1 & 2 & 3 & 4 \\\hline f ( x ) & 4 & 3 & 2 & 1 \\\hline\end{array}$$

A) $f ( 0 ) = 6$
B) $f ( 0 ) = - 5$
C) $f ( 0 ) = 1$
D) $f ( 0 ) = - 1$
E) $f ( 0 ) = 5$

Question 22

a) Find correlation coefficient to the set of data. Round the answer to 4 decimal places if necessary.
$\{ ( 1,3 ) , ( - 2,9 ) , ( 2,1 ) \}$
r = __________

b) Find correlation coefficient to the set of data. Round the answer to 4 decimal places if necessary.
$\{ ( 0,1 ) , ( 1,0 ) , ( 2,1 ) \}$
r = __________

c) Find correlation coefficient to the set of data. Round the answer to 4 decimal places if necessary.
$\{ ( 0,0 ) , ( 5 , - 5 ) , ( 2 , - 1.7 ) \}$
r = __________

Use correlation coefficients to determine which of the given sets of data is best fit by its associated regression line.

__________

Use correlation coefficients to determine which of the given sets of data is worst fit by its associated regression line .

Is it a perfect fit for any of the data sets

Question 23

Following are approximate values of the Amex Gold BUGS Index. ​
( represents 2000)
Complete the table. ​
Obtain the associated regression line. (Round coefficients to 2 decimal places if necessary.)
Slope: __________
Intercept: __________
Use your regression equation to project the 2001 sales. (Round the answer to 2 decimal places if necessary.)
__________

Question 24

A table of values for a linear function is given. Find $f ( 1 )$ . $$\begin{array} { | l | l | l | } \hline \boldsymbol { x } & - 1 & 0 \\\hline \boldsymbol { f } ( \boldsymbol { x } ) & 7 & 11 \\\hline\end{array}$$

A) $f ( 1 ) = - 7$
B) $f ( 1 ) = - 3$
C) $f ( 1 ) = 8$
D) $f ( 1 ) = 4$
E) $f ( 1 ) = 15$

Question 25

Sketch the straight line of the following equation. $y = 5 x - 3$

A)
B)
C)
D)

Question 26

The chart shows second quarter total retail e-commerce sales in the U.S. in 2001, 2003 and 2005 ( represents 2001). Find the regression line. Round coefficients to two decimal places. ​
y = __________ t + __________
Use the regression line to estimate second quarter retail e-commerce sales in 2002. Round your answers to two decimal places if necessary.
$__________ billion

Question 27

Find the best-fit line associated with the set of points.
​ , , ​
Please enter your answer as an equation of line in the form . Round m and b to the nearest hundredth if necessary.

Question 28

Find the best-fit line associated with the set of points.
​ , , , ​
Please enter your answer as an equation of line in the form . Round m and b to the nearest hundredth if necessary.

Question 29

In 2004 the Texas Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The table gives the approximate number of jobs for the citizens of Texas that would be created at various levels of recovery. Find the regression line. ​
y = __________ x + __________
Use the regression line to estimate the number of jobs that would be created at a recovery level of 31%. Round your answers to three decimal places if necessary. ___________ million jobs

Question 30

Find the coefficient of correlation of the line that best fits the data set.
​ ​
Please give the answer to four decimal places if necessary.

Question 31

Find the coefficient of correlation of the line that best fits the data set.
​ ​
Please give the answer to four decimal places if necessary.

Question 32

Find the best-fit line associated with the set of points.
​
​ , , , ​
Please enter your answer as an equation of line in the form . Round m and b to the nearest hundredth if necessary.

Question 33

Find the coefficient of correlation of the line that best fits the data set.
​ ​
Please give the answer to four decimal places if necessary.

Question 34

Find the best-fit line associated with the set of points.
​ , , ​
Please enter your answer as an equation of line in the form . Round m and b to the nearest hundredth if necessary.

Question 35

A table of values for a linear function is given. Find $$f ( 5 )$$ . $$\begin{array} { | l | l | l | } \hline \boldsymbol { x } & 2 & 3 \\\hline \boldsymbol { f } ( \boldsymbol { x } ) & 7 & 2 \\\hline\end{array}$$

A) $f ( 5 ) = - 12$
B) $f ( 5 ) = 42$
C) $f ( 5 ) = - 8$
D) $f ( 5 ) = 25$
E) $f ( 5 ) = - 7$

Question 36

Find the equation of the given linear function. $$\begin{array} { | l | l | l | l | l | } \hline \boldsymbol { x } & - 2 & 0 & 2 & 4 \\\hline \boldsymbol { f } ( \boldsymbol { x } ) & 5 & 1 & - 3 & - 7 \\\hline\end{array}$$

A) $f ( x ) = - 1 + 2 x$
B) $f ( x ) = 1 - 2 x$
C) $f ( x ) = 4 - 2.1 x$
D) $f ( x ) = 4 - 2 x$
E) $f ( x ) = 1 + 2.7 x$

Question 37

Sketch the straight line with the equation. $6 x = 12$

A)
B)
C)
D)
E)

Question 38

Decide which of the two given functions is linear and find its equation. $$\begin{array} { | l | l | l | l | l | l | } \hline \boldsymbol { x } & 0 & 1 & 2 & 3 & 4 \\\hline f ( x ) & 1 & - 1.5 & - 4 & - 6.5 & - 9 \\\hline \boldsymbol { g } ( \boldsymbol { x } ) & 1 & - 2 & - 5 & - 8 & - 10 \\\hline\end{array}$$

A) $f ( x ) = 4 + 3 x$
B) $g ( x ) = 1 - 3 x$
C) $g ( x ) = 1 + 2.5 x$
D) $f ( x ) = 4 - 3 x$
E) $f ( x ) = 1 - 2.5 x$

Question 39

Find the coefficient of correlation of the line that best fits the data set.
​ ​
Please give the answer to four decimal places if necessary.

Question 40

Following are forecasts of worldwide annual cell phone handset sales. ​
( represents 2003)
Complete the table. ​
Obtain the associated regression line. (Round coefficients to 2 decimal places if necessary.)
Slope: __________
Intercept: __________
Use your regression equation to project the 2016 sales. (Round the answer to 2 decimal places if necessary.)
__________

Question 41

Sketch the straight line with the equation. $20 y = 30$

A)
B)
C)
D)
E)

Question 42

The demand for your college newspaper is 1800 copies per week if the paper is given a way free of charge, and the demand drops to 900 if the charge is $0.10 per copy. However, the university is prepared to supply only 700 copies per week free of charge but will supply 950 per week at $0.25 per copy. At what price should the college newspapers be sold so that there is neither a surplus nor a shortage of papers ?

A)$0.07
B) $0.06
C) $0.22
D) $0.17
E) $0.11

Question 43

Annual federal spending on Medicare increased more or less linearly from $45 billion in 1973 to $87 billion in 1994. Use these data to express s, the annual spending on Medicare (in billions of dollars), as a linear function of t, the number of years since 1973.

A) $s = 2 t + 42$
B) $s = 87 t + 45$
C) $s = 2 t + 87$
D) $s = 45 t + 2$
E) $s = 2 t + 45$

Question 44

Find the linear equation that is the straight line through (5, 5) and parallel to the line $12 x - 6 y = 19$ .

A) $y = x$
B) $y = 2 x - 15$
C) $y = x - 5$
D) $y = 2 x + 5$
E) $y = 2 x - 5$

Question 45

The position of a model train, in feet along the railroad track, is given by $s ( t ) = 3.5 t + 3$ after t seconds.
Where is the train after 10 seconds

A)13 feet
B) 38 feet
C) 16.5 feet
D) 65 feet
E) 35 feet

Question 46

Calculate the slope of the straight line through the points $( - 1,0 )$ and $\left( - \frac { 7 } { 8 } , \frac { 1 } { 4 } \right)$ . Try to do the calculation mentally.

A) $m = 2$
B) $m = 7$
C) $m = - \frac { 2 } { 15 }$
D) $m = - \frac { 1 } { 2 }$
E) $m = \frac { 1 } { 7 }$

Question 47

A piano manufacture has a daily fixed cost of $1,300 and a marginal cost of $1,600 per piano. On a given day, what is the cost of manufacturing 3 pianos ?

A) $3,500
B) $8,700
C) $6,100
D) $5,500

Question 48

You can sell 90 pet chias per week if they are marked as $1 each, but only 40 per week if they are marked $2 per chia. Your chia supplier is prepared to sell you 25 chias per week if they are marked $1 per chia, and 75 per week if they are marked $2 per chia. Write the associated linear demand and supply functions.

A) $q = - 50 p + 140$ , $s = 50 p + 25$
B) $q = - 50 p + 140$ , $s = - 50 p + 25$
C) $q = - 50 p + 140$ , $s = 50 p - 25$
D) $q = - 50 p - 140$ , $s = - 50 p + 75$
E) $q = 50 p - 140$ , $s = - 50 p - 75$

Question 49

You can sell 60 pet chias per week if they are marked as $1 each,but only 50 per week if they are marked $2 per chia. Your chia supplier is prepared to sell you 10 chias per week if they are marked $1 per chia, and 20 per week if they are marked $2 per chia. At what price should the chias be marked so that there is neither surplus nor a shortage of chias ?

A)$3.50
B) $3.64
C) $2.25
D) $3.55
E) $4.50

Question 50

Sketch the straight line with the equation. $25 x = - 5 y$

A)
B)
C)
D)
E)

Question 51

Estimate the slope of the line segment.

A) $m = \frac { 1 } { 5 }$
B) $m = \frac { 1 } { 2 }$
C) $m = 2$
D) $m = \frac { 2 } { 5 }$
E) $m = \frac { 5 } { 2 }$

Question 52

U.S. imports of pasta increased from 290 million pounds in 1990 $( t = 0 )$ , by an average of 52 million pounds per year. Estimate U.S. pasta import (in million pounds) in the year 2005, assuming the import trend continued.

A)2,295 million pounds
B) 1,122 million pounds
C) 342 million pounds
D) 780 million pounds
E) 1,070 million pounds

Question 53

Calculate the slope of the straight line through the points $( 2,1 )$ and $( 5,10 )$ . Try to do the calculations mentally.

A) $m = 9$
B) $m = - 3$
C) $m = \frac { 1 } { 3 }$
D) $m = - \frac { 1 } { 3 }$
E) $m = 3$

Question 54

Find the linear equation that is the straight line through (25, -1) and increasing at a rate of 5 units of y per unit of x.

A) $y = 5 x + 127$
B) $y = 5 x - 127$
C) $y = 5 x - 126$
D) $y = 127 x + 126$
E) $y = 126 x - 127$

Question 55

Estimate the slope of the line segment.

A) $m = 0$
B) $m = - \frac { 1 } { 2 }$
C) $m = y$
D) $m = \frac { 1 } { 2 }$
E) Undefined

Question 56

A piano manufacture has a daily fixed cost of $1,000 and a marginal cost of $1,500 per piano. Find the cost C of manufacturing x pianos in one day.

A) $C ( x ) = 1,500 x - 1,000$ per day
B) $C ( x ) = 1,000 x - 1,500$ per day
C) $C ( x ) = 1,500 x$ per day
D) $C ( x ) = 1,000 x + 1,500$ per day
E) $C ( x ) = 1,500 x + 1,000$ per day

Question 57

Calculate the slope of the straight line through the points (4, 3) and (9, 13).

A) $m = \frac { 16 } { 13 }$
B) $m = \frac { 1 } { 2 }$
C) $m = 1.3$
D) $m = 3$
E) $m = 2$

Question 58

Find the linear equation that is the straight line through $\left( 0 , - \frac { 1 } { 2 } \right)$ with slope $\frac { 1 } { 8 }$ .

A) $y = \frac { 1 } { 8 } x - \frac { 1 } { 2 }$
B) $y = \frac { 1 } { 8 } x + \frac { 1 } { 2 }$
C) $y = \frac { 1 } { 2 } x - \frac { 1 } { 8 }$
D) $y = \frac { 1 } { 8 } x - 2$
E) $y = \frac { 1 } { 2 } x - 8$

Question 59

Find the linear equation that is the straight line through (1, 2) and (8, 30).

A) $y = 4 x + 2$
B) $y = 7 x - 2$
C) $y = 4 x - 7$
D) $y = 4 x - 6$
E) $y = 4 x - 2$

Question 60

Find the linear equation that is the straight line through $( 4,5 )$ with slope 5.

A) $y = 5 x + 15$
B) $y = 5 x - 25$
C) $y = 5 x - 20$
D) $y = 5 x + 20$
E) $y = 5 x - 15$

Question 61

A police car was traveling down Ocean Parkway in a high-speed chase from Jones Beach. The car was at Jones Beach at exactly 9:00 p.m. $( t = 0 )$ , and was at Oak Beach, 13 miles from Jones Beach, at exactly 9:04 p.m. How fast was the police car traveling (Round your answer to the nearest tenth.)

A)2.6 miles/min.
B) 4.3 miles/min.
C) 3.3 miles/min.
D) 2.5 miles/min.
E) 3.0 miles/min.

Question 62

The position of a model train, in feet along the railroad track, is given by $s ( t ) = 3 t + 3$ after t seconds.
When will the train have moved a distance of 33 feet

A)after 30 seconds
B) after 10 seconds
C) after 13 seconds
D) after 12 seconds
E) after 11 seconds

Question 63

The demand for your college newspaper is 2,000 copies per week if the paper is given a way free of charge, and the demand drops to 1,000 if the charge is $0.25 per copy. However, the university is prepared to supply only 600 copies per week free of charge but will supply 3,600 per week at $0.50 per copy. At what price should the college newspapers be sold so that there is neither a surplus nor a shortage of papers Round your answer to two decimal places.
$ __________

Question 64

Estimate the slope of the line segment.
​
​

Question 65

You can sell 45 pet chias per week if they are marked as $4 each,but only 20 per week if they are marked $5 per chia.Your chia supplier is prepared to sell you 10 chias per week if they are marked $4 per chia, and 35 per week if they are marked $5 per chia. At what price should the chias be marked so that there is neither surplus nor a shortage of chias Round your answer to two decimal places. $ __________

Question 66

The height of the falling sheet of paper, in feet from the ground, is given by $s ( t ) = - 1.5 t + 9$ after t seconds.
When will the sheet of paper reach the ground

A)after 9 seconds
B) after 7.5 seconds
C) after 15 seconds
D) after 6 seconds
E) after 3 seconds

Question 67

The Oliver company plans to market a new product. Based on its market studies, Oliver estimates that it can sell up to 5,000 units in 2005. The selling price will be $2 per unit. Variable costs are estimated to be 20% of total revenue. Fixed costs are estimated to be $5,600 for 2005. How many units should the company sell to break even ?

A)5,000 units
B) 5,600 units
C) 2,333 units
D) 3,500 units
E) 2,800 units

Question 68

Calculate the slope of the straight line through the points (3, 3) and (8, 18). Try to do the calculations mentally.

Question 69

In the Fahrenheit temperature scale, water freezes at 32°F and boils at 212°F. In the Celsius (or centigrade) scale, water freezes at 0°C and boils at 100°C. Assuming that the Fahrenheit temperature F and the Celsius temperature C are related by a linear equation, find the Fahrenheit temperature that correspond to 26°C, to the nearest degree. ​

A)​46°F
B) 104°F
C) 79°F
D) 47°F
E) 58°F

Question 70

A car that was being pursued by the police was at Jones Beach at exactly 7:57 p.m. $( t = 0 )$ , and passed Oak Beach (13 miles from Jones Beach) at exactly 8:06 p.m.,where it was overtaken by the police. How fast, in miles per minute, was the car traveling (Round your answer to the nearest tenth.)

A) $2.2 \frac { \text { miles } } { \mathrm { min } }$

B) $1.0 \frac { \text { miles } } { \mathrm { min } }$

C) $1.3 \frac { \text { miles } } { \min }$

D) $1.4 \frac { \text { miles } } { \mathrm { min } }$

E) $2.2 \frac { \text { miles } } { \mathrm { min } }$ .

Question 71

A piano manufacture has a daily fixed cost of $1,400 and a marginal cost of $1,900 per piano. On a given day, what is the cost of manufacturing 3 pianos $ __________

Question 72

Following are some approximate values of the Amex Gold BUGS Index. $\begin{array} { | l | l | l | l | } \hline \text { Year } & 1995 & 2000 & 2004 \\\hline \text { Index } & 200 & 50 & 250 \\\hline\end{array}$

Take t to be the year since 1995 and y to be the BUGS index.
Obtain a piecewise linear model of the gold BUGS index for 1995-2004.

A) $y = \left\{ \begin{array} { l l } 30 t + 200 & \text { if } 0 \leq t \leq 5 \\50 t - 200 & \text { if } 5 < t \leq 9\end{array} \right.$
B) $y = \left\{ \begin{array} { l l } - 30 t + 200 & \text { if } 0 \leq t \leq 5 \\50 t + 200 & \text { if } 5 < t \leq 9\end{array} \right.$
C) $y = \left\{ \begin{array} { l l } - 30 t + 200 & \text { if } 0 \leq t \leq 5 \\50 t - 200 & \text { if } 5 < t \leq 9\end{array} \right.$
D) $y = \left\{ \begin{array} { l l } 50 t + 200 & \text { if } 0 \leq t \leq 5 \\- 30 t - 200 & \text { if } 5 < t \leq 9\end{array} \right.$
E) $y = \left\{ \begin{array} { l l } 50 t + 200 & \text { if } 0 \leq t \leq 5 \\- 30 t + 200 & \text { if } 5 < t \leq 9\end{array} \right.$

Question 73

In the Fahrenheit temperature scale, water freezes at 32°F and boils at 212°F. In the Celsius (or centigrade) scale, water freezes at 0°C and boils at 100°C. Assuming that the Fahrenheit temperature F and the Celsius temperature C are related by a linear equation, find the Celsius temperature that correspond to 39°F, to the nearest degree. ​

A)54°C
B) 7°C
C) 4°C
D) 39°C
E) 38°C

Question 74

Calculate the slope of the straight line through the points and . Try to do the calculations mentally.

Question 75

The linear function is given. Find .

Question 76

The position of a model train, in feet along the railroad track, is given by $s ( t ) = 1.5 t + 12$ after t seconds.

Where is the train after 2 seconds

__________ feet

Question 77

Calculate the slope of the straight line through the points (2.6, 5) and (6.6, -3). Try to do the calculations mentally.

Question 78

The Snowtree cricket behaves in a rather interesting way: The rate at which it chirps depends linearly on the temperature. One summer evening you hear a cricket chirping at a rate of 140 chirps per minute, and you notice that the temperature is 80°F. Later in the evening, the cricket has slowed down to 120 chirps per minute, and you notice that the temperature has dropped to 75°F. What is the temperature if the cricket is chirping at a rate of 108 chirps per minute ?

A)72°F
B) 70°F
C) 78°F
D) 67°F
E) 76°F

Question 79

In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model ​N as a piecewise linear function of the time t in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1965. (Round you answer to the nearest integer.) ​

A)169 people per thousand
B) 219 people per thousand
C) 203 people per thousand
D) 152 people per thousand
E) 118 people per thousand

Question 80

U.S. imports of pasta increased from 290 million pounds in 1990 (t = 0), by an average of 52 million pounds per year. Estimate U.S. pasta import (in million pounds) in the year 2010, assuming the import trend continued.
​
__________ million pounds