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x y
900 70
988 80
1000 82
1010 84
1200 105
1205 108

y = 0. 121 x 38.841 , r = 0.998

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Extensions

Graph f ( x ) = 0.5 x + 10 . Pick a set of 5 ordered pairs using inputs x = −2 ,  1 ,  5 ,  6 ,  9 and use linear regression to verify that the function is a good fit for the data.

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Graph f ( x ) = 2 x 10 . Pick a set of 5 ordered pairs using inputs x = −2 ,  1 ,  5 ,  6 ,  9 and use linear regression to verify the function.

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −2 0 ) , ( 6 , −22 ) , ( 9 , −28 ) ; y = −2 x −10

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For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years:

( 46 ,  1 , 6 00 ) ,   ( 48 ,  1 , 55 0 ) ,   ( 5 0 ,  1 , 5 0 5 ) ,   ( 52 ,  1 , 54 0 ) ,   ( 54 ,  1 , 495 ) .

Use linear regression to determine a function P where the profit in thousands of dollars depends on the number of units sold in hundreds.

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Find to the nearest tenth and interpret the x -intercept.

( 189 . 8 , 0 )   If 18,980 units are sold, the company will have a profit of zero dollars.

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Find to the nearest tenth and interpret the y -intercept.

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Real-world applications

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:

(2500, 2000), (2650, 2001), (3000, 2003), (3500, 2006), (4200, 2010)

Use linear regression to determine a function y , where the year depends on the population. Round to three decimal places of accuracy.

y = 0.00587 x + 1985 .4 1

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Predict when the population will hit 8,000.

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For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:

( 46 ,  25 0 ) ,   ( 48 ,  3 0 5 ) ,   ( 5 0 ,  35 0 ) ,   ( 52 ,  39 0 ) ,   ( 54 ,  41 0 ) .

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .

y = 2 0. 25 x 671 . 5

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Predict when the profit will exceed one million dollars.

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For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:

(46, 250), (48, 225), (50, 205), (52, 180), (54, 165) .

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .

y = 1 0. 75 x + 742 . 5 0

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Predict when the profit will dip below the $25,000 threshold.

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Chapter review exercises

Linear Functions

Determine whether the algebraic equation is linear. 2 x + 3 y = 7

Yes

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Determine whether the algebraic equation is linear. 6 x 2 y = 5

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Determine whether the function is increasing or decreasing.

f ( x ) = 7 x 2

Increasing.

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Questions & Answers

find the equation of the tangent to the curve y=2x³-x²+3x+1 at the points x=1 and x=3
Esther Reply
derivative of logarithms function
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ex 2.1 question no 11
khansa
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ex 2.1 question no. 11
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Find the derivative of g(x)=−3.
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abdulkadir
f(x) = x-2 g(x) = 3x + 5 fog(x)? f(x)/g(x)
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fog(x)= f(g(x)) = x-2 = 3x+5-2 = 3x+3 f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
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find the bounded area of the parabola y^2=4x and y=16x
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what is absolute value means?
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Chicken nuggets
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🐔🦃 nuggets
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(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |. The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
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find integration of loge x
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find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
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Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
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log tan (x/4+x/2)
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y=(x^2 + 3x).(eipix)
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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