Question

The table shows the profits (y) in millions of dollars for Buffalo Wild Wings for each year (x) from 2007 through 2013, where x=7 represents 2007.
Year x | Profits y
7 | 19.7
8 | 24.4
9 | 30.7
10 | 38.4
11 | 50.4
12 | 57.3
13 | 71.6


a.) sketch a graph

b.) use the slopes to determine the years in which the profits showed the greatest or least increases.

c.) find the equation of a line between 2007 and 2013

d.) interpret meaning of the slope and line from part (c) in the context of the problem

e) use the equation from part (c) to estimate the profit for Buffalo wild wings in 2017. Do you think that it is an accurate estimate. Explain.

Answer 1

a) See attached diagram.

b) The slope can be obtained by the formula:

$m_i=\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i}.$

Now

• $m_1=\dfrac{24.4-19.7}{8-7}=4.7;$
• $m_2=\dfrac{30.7-24.4}{9-8}=6.3;$
• $m_3=\dfrac{38.4-30.7}{10-9}=7.7;$
• $m_4=\dfrac{50.4-38.4}{11-10}=12;$
• $m_5=\dfrac{57.3-50.4}{12-11}=6.9;$
• $m_6=\dfrac{71.6-57.3}{13-12}=14.3;$

The greatest increases were from 2012 till 2013 years and the least increases were from 2007 till 2008 years.

c) Using graphing calculator, the equation of the line (black line in the diagram) is

$y\approx 0.71x^2-5.58x+23.76.$

d) Since the slopes are different, this line is not straight. From the given data you can predict that the "best fit" is quadratic function.

e) In 2017, find

$y(17)\approx 0.71\cdot 17^2-5.58\cdot 17+23.76\approx 134.09$