Chapter 2.2, Problem 74E

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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

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

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,

Here,

The formula for linear model is,

Here,

**Calculation:**

Consider the given statement,

The annual revenue increases from

Thus, coordinates for the models are

Consider the expression of linear model,

Here *x* represents time since 2000.

Substitute

Similarly substitute

Subtract the expression

Divide both side by 4.

Substitute

Subtract 35.2 on both side of the equation

**(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

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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