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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

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 2010.17

a. 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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