   Chapter 2.2, Problem 74E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Revenue The annual revenue of Amazon rose from approximately $10.7 billion in 2006 to$34.2 billion in 2010.17a. Use this information to find both a linear model and an exponential model for Amazon's annual revenue I (in billions of dollars) as a function of time tin years since 2000. (Round all coefficients to three significant digits.) [HINT: See Example 2.] Which of these models would you judge to be more appropriate to the data shown below? Year t (years since 2000) 6 7 8 9 10 Annual Revenue I ($billion) 10.7 14.8 19.2 24.5 34.2 b. Use the better of the two models from part (a) to predict the 2008 figure, and compare it with the actual figure above. (a) To determine To calculate: The linear and exponential model for the Amazon’s annual revenue I (in billions of dollars) as a function of time t in years since 2000 if the annual revenue increases from$10.7 billion in 2006 to $34.2 billion in 2010. Also decide which model is more appropriate for following data shown below:  Years t (year since 2000) 6 7 8 9 10 Annual revenue I ($ billion) 10.7 14.8 19.2 24.5 34.2
Explanation

Given Information:

The annual revenue increases from $10.7 billion in2006 to$34.2 billion in 2010.

The data table is,

 Years t (year since 2000) 6 7 8 9 10 Annual revenue I ($billion) 10.7 14.8 19.2 24.5 34.2 Formula used: The formula for exponential model is, y=Abx Here, A and b are constants. The formula for linear model is, y=mx+c Here, m and c are constants. Calculation: Consider the given statement, The annual revenue increases from$10.7 billion in 2006 to $34.2 billion in 2010. Thus, coordinates for the models are (6,10.7) and (10,34.2). Consider the expression of linear model, y=mx+c Here x represents time since 2000. Substitute x=6 and y=10.7 in the expression y=mx+c. 10.7=m(6)+c10.7=6m+c6m+c=10.7 Similarly substitute x=10 and y=34.2 in the expression y=mx+c. 34.2=m(10)+c34.2=10m+c Subtract the expression 6m+c=10.7 from the equation 10m+c=34.2. 10m+c=34.2 6m+c=10.7_ 4m=23.5 Divide both side by 4. 4m4=23.54m=5.86 Substitute m=5.86 in the expression 6m+c=10.7. 6(5.86)+c=10.735.2+c=10.7 Subtract 35.2 on both side of the equation 35.2+c35.2=10.735 (b) To determine To calculate: The projected figure of 2008 from the best model between linear and exponential model if the annual revenue increases from$10.7 billion in2006 to $34.2 billion in 2010. Also to decide which model is more appropriate for following data  Years t (year since 2000) 6 7 8 9 10 Annual revenue I ($ billion) 10.7 14.8 19.2 24.5 34.2

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