Quiksilver, Inc., the makers of the Quiksilver and Roxy clothing lines, has had steadily increasing profits over the past several years. The profits for Quiksilver, Inc. are given in the chart.

Question

A bar chart with 5 bars of unequal heights is titled "Gross Profits for Quicksilver, Inc." The horizontal axis is labeled "Year." The vertical axis is labeled "Gross profit (millions of dollars)" From left to right, the bars are as follows.

1. The first bar is labeled 2002 and has a height of 286.3.
2. The second bar is labeled 2003 and has a height of 454.4.
3. The third bar is labeled 2004 and has a height of 605.0.
4. The fourth bar is labeled 2005 and has a height of 850.4.
5. The fifth bar is labeled 2006 and has a height of 1147.2.

(b) Find an equation for a model of these data. (Use the second and fifth values in the chart to calculate your equation. Round the slope and the y-intercept to one decimal place.)

 

 

 

(c) Use the adjusted model P = 215t − 200

 to estimate the profit for Quiksilver, Inc. in 2012.

The gross profit for Quiksilver, Inc. in 2012 would be about  

.

(d) Give a reasonable domain and range for this model.

Domain:

Answer 1

(b)

x is the number of years since 2002.

(1, 454.4)

(4, 1147.2)

slope m = (1147.2 - 454.4)/ (4-1) = 692.8/3 = 230.93

intercept B = y - mx = 454.4 - (230.93)*1 = 223.46

So this model is y = 230.9x - 223.5, rounded to one decimal place as directed

(c) 2012 - 2002 = 10

P = 215*10 - 200 = 2150-200 = 1950

(d) the domain is the set of positive integers representing the year since 2002.

the range is the set of real numbers, representing the profit.

for part (a) you may use technology such as spreadsheet to create the bar graph.

using the model for part B, 230.9*10 -223.5 = 2309 - 223.5 = 2085.5

The difference between the models is (2085.5 - 1950)*100%/1950 = 6.843% difference