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# Help with function problems

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thanks so much

Feb 7, 2018
edited by Guest  Feb 8, 2018

#1
+100571
+1

We need to find the x coordinate  of A, thusly

20 =  (-1/2)x^2 - x + 30

Subtract 20 from both sides  and rearrange

(-1/2)x^2 - x + 10  =  0       multiply through by -2

x^2  + 2x - 20  =  0

Using the quadratic formula to find the solutions  of this and taking the negative value, we have that

x  =  -1 - √21

So     ( -1 - √21, 20) is one point on the line

And to find the y values associated with B we have

(-1/2)(5)^2 - 5 + 30   =  -25/2 + 25   =   12.5

So   the point (5, 12.5)  is also on the graph

So  the slope is   [ 20 - 12.5 ]  / [  -1 - √21 - 5 ]  =  [ -7.5] / [ 6 + √21 ]

So......the equation of the line  is

y  =  (  [ -7.5] / [ 6 + √21 ] )  ( x - 5)  + 12.5

Feb 7, 2018
#2
+100571
+1

2.)

a)  The profit of a company was \$10 million in 2006 and \$20.6 million in 2012. Find a linear model to represent the profit P of the company (in millions of dollars) in function of t . Variable t represents the number of year after 2004.

b)  Interpret the meaning of the model’s slope in the context of the problem. Include units in your interpretation.

a)  We have the points   [ 2, 10]  and [ 8, 20.6]

The slope is    [ 20.6 - 10 ]  / [ 8 - 2 ]  =  10.6 / 6   =  53/30

The linear model is

y = (53/30) ( t - 2) + 10

y = (53/30)t  -  53/15  + 10

y =  (53/30)t + 97/ 15

b)  The slope, (53/30)  indicates the profit is increasing by  ≈  \$ 1.76 M    per year

Feb 7, 2018