Exam 1: Functions and Applications

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 ?

Function f is $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } & \text { if } - 16 < x \leq 0 \\\sqrt { x } & \text { if } 0 < x \leq 41\end{array} \right.$ . Find $f ( 36 )$ .

Function f is $f ( x ) = \left\{ \begin{array} { l l } 7 x & \text { if } 0 < x < 10 \\x + 8 & \text { if } 10 \leq x < 20 \\7 x & \text { if } 20 \leq x \leq 30\end{array} \right.$ Find $f ( 14 )$

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 $ __________

Choose the graph of the function $f ( x ) = - \frac { x ^ { 3 } } { 5 }$ , domain $( - \infty , \infty )$ from the following:

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.

Following are forecasts of worldwide annual cell phone handset sales. Year 3 5 7 Sales (Millions) 500 600 800 ( $x = 3$ represents 2003) Obtain the associated regression line. (Round coefficients to 2 decimal places if necessary.) Use your regression equation to project the 2017 sales.

Graph shows the number of sports utility vehicles $f ( t )$ sold in the United States. $f ( t )$ represents sales in year t in thousands of vehicles. Find $f ( 4 )$ .

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

Find the coefficient of correlation of the line that best fits the data set. ​ $\{ ( 0,2 ) , ( 2,5 ) , ( - 8,19 ) \}$ ​ Please give the answer to four decimal places if necessary.

Find the linear equation that is the straight line through (4, 4) and (9, 19). ​ Please enter your answer as an equation in the form $y = m x + b$ .

Choose the graph of the function $f ( x ) = 8 \sqrt [ 3 ] { x }$ , domain $( - \infty , \infty )$ from the following:

Use the graph of the function f to find $f ( 1 )$ .

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

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

If the revenue R is specified as a function of selling price ?s, which variable is independent ?

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

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

Following are some approximate values of the Amex Gold BUGS Index. Year 1995 2000 2004 Index 200 50 250 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.

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. Percent Recovery (\%) - 20 40 80 100 Jobs Created (Millions) 3 6 9 15 ​ 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. $y ( 31 ) =$ ___________ million jobs