Exam 1: Functions and Applications

Following are approximate values of the Amex Gold BUGS Index. Year 0 2 4 Index 50 100 250 ​ ( $x = 0$ represents 2000) Complete the table. x y xy 0 50 2 100 4 250 Totals ​ 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.) __________

Estimate the slope of the line segment.

Function $f$ is $f ( x ) = \left\{ \begin{array} { c } x ^ { 2 } \quad \text { if } - 13 < x \leq 0 \\\sqrt { x } \text { if } 0 < x \leq 49\end{array} \right.$ . Find $f ( 9 )$ .

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 ?

The linear function is given. Find $f ( 0 )$ . 1 2 3 4 ( ) 2.5 0 -2.5 -5

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

If the income I is specified as a function of selling price s, which variable is independent and which one is dependent? Choose the correct letter for each question. -Independent variable

Write the equation $y = 5 x ^ { 2 } - 4$ using function notation.

Choose the graph of the function $f ( x ) = \frac { x ^ { 4 } } { 6 }$ , domain $( - \infty , \infty )$ from the following:

The percentage $p ( t )$ of children who are able to speak in at least single words by the age of t months can be approximated by the equation. $p ( t ) = 100 \left( 1 - \frac { 12,156 } { t ^ { 4.17 } } \right)$ What percent of children are able to speak in at least single words by the age of 14 months Round to the nearest percent.

Given $f ( x ) = x ^ { 2 } + 3 x + 4$ , find $f ( 3 )$ .

Estimate the slope of the line segment. ​ ​

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. $ __________

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. ​

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

The chart shows second quarter total retail e-commerce sales in the U.S. in 2001, 2003 and 2005 ( $t = 0$ represents 2001). Find the regression line. Round coefficients to two decimal places. Year 0 2 4 Sales (S Billion) 8 13 20 ​ 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

The linear function is given. Find $f ( 0 )$ . 1 2 3 4 f(x) 4 3 2 1

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 ?

You can sell 95 pet chias per week if they are marked as $1 each, but only 45 per week if they are marked $2 per chia. Your chia supplier is prepared to sell you 35 chias per week if they are marked $1 per chia, and 85 per week if they are marked $2 per chia. Write the associated linear demand and supply functions. ​ Please enter your answer as two equations, separated by a comma. Use the notation: q for demand, s for supply, and ​p for price.

The value of the Conference Board Index of 10 economic indicators in the U.S. could be approximated by the function of time t in months since the end of December 2002. $E ( t ) = \left\{ \begin{array} { l l } 0.4 t + 110 & \text { if } 6 \leq t \leq 15 \\- 0.2 t 119 & \text { if } 15 < t \leq 20\end{array} \right.$ Use the model to estimate when - prior to March, 2004 - the index was 113.