+130091 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
+130091 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
