Exam 1: Functions and Linear Models

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Estimate the slope of the line segment. Estimate the slope of the line segment.

(Multiple Choice)
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Decide which of the two given functions is linear and find its equation. Decide which of the two given functions is linear and find its equation.   Please enter your answer as an equation of a linear function. Please enter your answer as an equation of a linear function.

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The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 2003 can be approximated by The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 2003 can be approximated by   billion dollars (   is time in years since 1983). Find an appropriate domain of   . billion dollars ( The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 2003 can be approximated by   billion dollars (   is time in years since 1983). Find an appropriate domain of   . is time in years since 1983). Find an appropriate domain of The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 2003 can be approximated by   billion dollars (   is time in years since 1983). Find an appropriate domain of   . .

(Multiple Choice)
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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 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   and the Celsius temperature   are related by a linear equation, find the Celsius temperature that correspond to 68 F, to the nearest degree. and the Celsius temperature 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   and the Celsius temperature   are related by a linear equation, find the Celsius temperature that correspond to 68 F, to the nearest degree. are related by a linear equation, find the Celsius temperature that correspond to 68 F, to the nearest degree.

(Multiple Choice)
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You can sell 80 pet chias per week if they are marked as $4 each, but only 30 per week if they are marked $5 per chia. Your chia supplier is prepared to sell you 20 chias per week if they are marked $4 per chia, and 70 per week if they are marked $5 per chia. Write the associated linear demand and supply functions.

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Estimate the slope of the line segment. Estimate the slope of the line segment.   Please enter your answer as a fraction if necessary. Please enter your answer as a fraction if necessary.

(Short Answer)
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Find the linear equation that is the straight line through (1, 1)with slope 3.

(Multiple Choice)
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The percentage The percentage   of children who are able to speak in at least single words by the age of   months can be approximated by the equation.   What percent of children are able to speak in at least single words by the age of 11 months? Round to the nearest percent. of children who are able to speak in at least single words by the age of The percentage   of children who are able to speak in at least single words by the age of   months can be approximated by the equation.   What percent of children are able to speak in at least single words by the age of 11 months? Round to the nearest percent. months can be approximated by the equation. The percentage   of children who are able to speak in at least single words by the age of   months can be approximated by the equation.   What percent of children are able to speak in at least single words by the age of 11 months? Round to the nearest percent. What percent of children are able to speak in at least single words by the age of 11 months? Round to the nearest percent.

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Find the linear equation that is the straight line through (9, 5)and parallel to the line Find the linear equation that is the straight line through (9, 5)and parallel to the line   . .

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Find the best-fit line associated with the set of points. Find the best-fit line associated with the set of points.

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Calculate the slope of the straight line through the points (4.1, 1)and (9.1, -14). Try to do the calculations mentally.

(Short Answer)
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Use the graph of the function f to find Use the graph of the function f to find   .  . Use the graph of the function f to find   .

(Multiple Choice)
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Use technology (such as spreadsheet web site utilities, or a graphing calculator)to evaluate the function for Use technology (such as spreadsheet web site utilities, or a graphing calculator)to evaluate the function for   .   Round the answer to four decimal places if necessary. . Use technology (such as spreadsheet web site utilities, or a graphing calculator)to evaluate the function for   .   Round the answer to four decimal places if necessary. Round the answer to four decimal places if necessary.

(Multiple Choice)
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a)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary. a)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   r = __________ b)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   r = __________ c)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   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? __________ r = __________ b)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary. a)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   r = __________ b)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   r = __________ c)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   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? __________ r = __________ c)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary. a)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   r = __________ b)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   r = __________ c)Find correlation coefficient to the set of data. Round the answer to 4 decimal places, if necessary.   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? __________ 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? __________

(Short Answer)
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A table of values for a linear function is given. Find A table of values for a linear function is given. Find   .  . A table of values for a linear function is given. Find   .

(Multiple Choice)
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Given Given   , find   . , find Given   , find   . .

(Short Answer)
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The following table shows the approximate value V of one Euro in U.S, dollars from its introduction in January 2000 to January 2004. ( The following table shows the approximate value V of one Euro in U.S, dollars from its introduction in January 2000 to January 2004. (   represents January, 2000.)   Which model would best fit the given data? ( A , a , b , c , k , l , and m are constants.) represents January, 2000.) The following table shows the approximate value V of one Euro in U.S, dollars from its introduction in January 2000 to January 2004. (   represents January, 2000.)   Which model would best fit the given data? ( A , a , b , c , k , l , and m are constants.) Which model would best fit the given data? ( A , a , b , c , k , l , and m are constants.)

(Multiple Choice)
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Write the equation Write the equation   using function notation. using function notation.

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The position of a model train, in feet along the railroad track, is given by The position of a model train, in feet along the railroad track, is given by   after   seconds. Where is the train after 10 seconds? after The position of a model train, in feet along the railroad track, is given by   after   seconds. Where is the train after 10 seconds? seconds. Where is the train after 10 seconds?

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Given Given   , find   . , find Given   , find   . .

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