Exam 1: Functions and Applications

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. $p ( t ) = 100 \left( 1 - \frac { 12,188 } { t ^ { 4.42 } } \right)$ By what age are 70% of children speaking in at least single words Round your answer to the nearest month.

Function $f$ is $f ( x ) = \left\{ \begin{array} { c } 9 x \text { if } 0 \leq x < 16 \\3 \text { if } 16 \leq x < 32\end{array} \right.$ . Find $f ( 12 )$ .

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

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

Find the linear equation that is the straight line through $\left( 0 , - \frac { 1 } { 6 } \right)$ with slope $\frac { 1 } { 4 }$ . ​ Please enter your answer as an equation in the form $y = m x + b$ .

A car that was being pursued by the police was at Jones Beach at exactly 10:54 p.m. $( t = 0 )$ , and passed Oak Beach (13 miles from Jones Beach) at exactly 11:07 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. v = __________ miles/minute

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

Based on the following table, find $f ( - 2 )$ . x -3 -2 -1 0 1 2 3 f(x) 4 9 5 5 2 1.6 1.15

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

Given $f ( x ) = \sqrt { 15 + x ^ { 2 } }$ , find $f ( - 1 )$ .

Given $g ( s ) = s ^ { 2 } + \frac { 2 } { s }$ , find $g ( 2 )$ .

Function f is $f ( x ) = \left\{ \begin{array} { l l } 6 x & \text { if } 0 \leq x < 7 \\1 & \text { if } 7 \leq x < 14\end{array} \right.$ Find $f ( 12 )$ .

Based on the following table, find $f ( 1 )$ . f -3 -2 -1 0 1 2 3 f(x) 1 5 3 1 4 0.7 0.95

Find the linear equation for the straight line through (4, 3) with slope 5. $y = m x + b$ Please enter your answer as an equation in the form

Find the linear equation that is the straight line through (5, 4) and parallel to the line given. ​ $4 x - 2 y = 7$ ​ Please enter your answer as an equation in the form $y = m x + b$ .

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 ?

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 retirees per thousand people aged 20-64 in 2009. ​ Please enter your answer as a number without the units. Round your answer to the nearest integer.

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

Use technology (such as spreadsheet web site utilities, or a graphing calculator) to evaluate the function for $x = 4.4$ . $r ( x ) = \frac { 2 x ^ { 2 } - 7 } { 2 x ^ { 2 } + 7 }$ Round the answer to four decimal places if necessary.

Find the equation of the given linear function. -2 0 2 4 f(x) 5 1 -3 -7 ​ Please enter your answer as an equation of a linear function.