Exam 1: Functions and Applications

Following are forecasts of worldwide annual cell phone handset sales. Year x 3 5 7 Sales y (Millions) 500 600 800 ​ ( $x = 3$ represents 2003) Complete the table. x y xy 3 500 5 600 7 800 Totals ​ 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.) __________

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

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 $f ( 4 )$ .

Given $f ( x ) = \sqrt { 32 + x ^ { 2 } }$ , find $f ( 2 )$ .

Given $f ( x ) = 3 x - 7$ , find $f ( 10 )$ .

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

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

The position of a model train, in feet along the railroad track, is given by $s ( t ) = 2.5 t + 12$ after t seconds. When will the train have moved a distance of 37 feet t = __________ seconds

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. (a) Model the 1995 and 2000 data with a linear equation. y = __________ (b) Model the 2000 and 2004 data with a linear equation. y = __________ (c) Use the results of parts (a) and (b) to obtain a piecewise linear model of the gold BUGS index for 1995-2004. $y = \left\{ \begin{array} { l l } \_\_\_\_& \text { if } 0 \leq t \leq\_\_ \\\_\_\_\_& \text { if } \_\_< \mathrm { t } \leq 9\end{array} \right.$ (d) Use your model to estimate the index in 1999. y = __________

Choose the graph of the function $f ( x ) = \frac { x ^ { 3 } } { 5 }$ , domain $[ 0 , \infty )$ from the following:

The processor speed, in megahertz, of Intel processors could be approximated by the function of time t in years since the start of 1995. $P ( t ) = \left\{ \begin{array} { l l } 75 t + 200 & \text { if } 0 \leq t \leq 4 \\600 t - 1,900 & \text { if } 4 < t \leq 9\end{array} \right.$ Use the model to estimate when processor speeds first hit 3.2 gigahertz (1 gigahertz = 1,000 megahertz).

Find the linear equation that is the straight line through (21, -3.8) and increasing at a rate of 15 units of y per unit of x. ​ Please enter your answer as an equation in the form $y = m x + b$ .

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

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. Use the graph to estimate the largest value of $f ( t )$ for $( 2 \leq t \leq 5 )$ .

Find the best-fit line associated with the set of points. ​ ​ $( 0 , - 2 )$ , $( 1,3 )$ , $( 4,15 )$ , $( 5,19 )$ ​ Please enter your answer as an equation of line in the form $y = m x + b$ . Round m and b to the nearest hundredth if necessary.

Find the coefficient of correlation of the line that best fits the data set. ​ $\{ ( 1,2 ) , ( 5,6 ) , ( 7,8 ) \}$ ​ Please give the answer to four decimal places if necessary.

The height of the falling sheet of paper, in feet from the ground, is given by $s ( t ) = - 3 t + 12$ after t seconds. When will the sheet of paper reach the ground $t =$ __________ seconds

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. Year 0 2 4 Sales (S Billion) 4 8 13 Use the regression line to estimate second quarter retail e-commerce sales in 2000. Round your answer to two decimal places.

Given $f ( x ) = - 3 x + 7$ , find $f ( a + b )$ .

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.)