Exam 1: Functions and Applications

U.S. imports of pasta increased from 290 million pounds in 1990 (t = 0), by an average of 52 million pounds per year. Estimate U.S. pasta import (in million pounds) in the year 2010, assuming the import trend continued. ​ __________ million pounds

Choose the graph of the function $f ( x ) = \frac { x ^ { 4 } } { 3 }$ , domain $( - \infty , \infty )$ from the following:

The position of a model train, in feet along the railroad track, is given by $s ( t ) = 1.5 t + 12$ after t seconds. Where is the train after 2 seconds __________ feet

Decide which of the two given functions is linear and find its equation. 0 1 2 3 4 f(x) 5 2 -1 -4 -7 ( ) 5 3.5 2 0.5 0 ​ Please enter your answer as an equation of a linear function.

A table of values for a linear function is given. Find $f ( 5 )$ . 2 3 ( ) 7 2

Choose the graph of the function $f ( x ) = 3 x$ , $( - 3 \leq x \leq 3 )$ from the following:

Use correlation coefficients to determine which of the given sets of data is worst fit by its associated regression line. a) $\{ ( 2,6 ) , ( - 4,18 ) , ( 4,2 ) \}$ b) $\{ ( 0,1 ) , ( 1,0 ) , ( 2,1 ) \}$ c) $\{ ( 0,0 ) , ( 5 , - 5 ) , ( 2 , - 2.2 ) \}$

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 104 chirps per minute __________ °F

Find the coefficient of correlation of the line that best fits the data set. ​ $\{ ( 0,0 ) , ( 3,14 ) , ( 6,21 ) \}$ ​ Please give the answer to four decimal places if necessary.

The table shows soybean production, in millions of tons, in Brazil's Cerrados region, as a function of the cultivated area, in millions of acres. Use technology to obtain the regression line. Round coefficients to two decimal places. Area (Millions of Acres) 25 30 32 40 52 Production (Millions of Tons) - 14 25 30 40 60

Given $f ( x ) = x ^ { 2 } + 4 x + 1$ , find $f ( - 3 )$ .

The table shows the number of fiber-optic cable connections to homes in the U.S. from 2000 to 2004 ( $t = 0$ represents 2000). Use technology to obtain the linear regression line, with regression coefficients rounded to two decimal places. Year t 0 1 2 3 4 Connections c (Thousands) 0 10 25 65 150

Find the best-fit line associated with the set of points. ​ $( 3,9 )$ , $( 5,16 )$ , $( 7,20 )$ , $( 9,0 )$ ​ 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 regression line associated with the set of points. Round all coefficients to 4 decimal places. $( 1,1 )$ , $( 2,1 )$ , $( 4,2 )$

Estimate the slope of the line segment.

Find the linear equation that is the straight line through (1, 2) and (8, 30).

U.S. imports of pasta increased from 290 million pounds in 1990 $( t = 0 )$ , by an average of 52 million pounds per year. Estimate U.S. pasta import (in million pounds) in the year 2005, assuming the import trend continued.

You can sell 60 pet chias per week if they are marked as $1 each,but only 50 per week if they are marked $2 per chia. Your chia supplier is prepared to sell you 10 chias per week if they are marked $1 per chia, and 20 per week if they are marked $2 per chia. At what price should the chias be marked so that there is neither surplus nor a shortage of chias ?

The following table shows the approximate average household income in the U.S. in 1990, 2002, and 2003. ( $t = 0$ represents 1990.) (Year) 0 12 13 (Household Income in \1 000) 30 42 43 Which of the following kinds of models would best fit the given data (A, a, b, c, and m are constants.)

Given $f ( x ) = - 2 x - 7$ , find $f ( 1 )$ .