and December retail sales, excluding autos for the years 2001-2009 can be modele

Question

and December retail sales, excluding autos for the years 2001-2009 can be modeled by the t nction so·-1681 2 + 3830 0x + 388.178 billion dollars, where x is te number of years after 2000 a. Graph the function for values of x representing 2001-2009 b. During what years does the model estimate the sales to be $540 billion? c. The recession in 2008 caused retail sales to drop. Does the model agree with the facts, that is, does it indicate that a maximum occurred in 20087 A. O B. O C. O D. Clear All emaining

Explanation / Answer

First question is answered below.

a)

Graph C represents the given model.

This is because at higher levels of x, S is decreasing, after an initial increase.

b)

S = -1.681x2 + 38.3x + 388.178

540 =-1.681x2 + 38.3x + 388.178

0 = -1.681x2 + 38.3x -151.822

Using quadratic equation solver, x = 5.11 / 17.67

So, in either in 2005 or 2017-2018, the sales will reach $540 billion

c)

Derivate S(x) with respect to x and put it equal to 0

This gives, -3.362x + 38.3 = 0

This gives x = 11.4

Thus, max occurred in 2011 and not 2008

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