Chapter 2.2, Problem 97E

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7th Edition

Stefan Waner + 1 other

ISBN: 9781337274203

Textbook Problem

Facebook The following table gives the approximate numbers of **Facebook** members at various times early in its history.^{32}

Year t (since start of 2005) |
0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 |

Facebook Members n (millions) |
1 | 2 | 5.5 | 7 | 12 | 30 | 58 | 80 |

**a.** Use exponential regression to model Facebook membership as a function of time in years since the start of 2005, and graph the data points and regression curve. (Round coefficients to three decimal places.)

**b.** Fill in the missing quantity: According to the model, Facebook membership each year was _________ times that of the year before.

**c.** Use your model to estimate Facebook membership in early 2009 to the nearest million.

**(a)**

To determine

**To calculate:** The regression model and the regression curve by using exponential regression to model Facebook membership as a function of time *t* since 2005 if the number of Facebook members at various times early in its history is shown by the provided table.

Explanation

**Given Information:**

The number of Facebook members at various times early in its history is shown by following table,

Year t(Since start of 2005) |
0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 |

Facebook Members n (million) |
1 | 2 | 5.5 | 7 | 12 | 30 | 58 | 80 |

**Calculation:**

Consider the number of Facebook members at various times early in its history is shown by following table,

Year t(Since start of 2005) |
0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 |

Facebook Members n (million) |
1 | 2 | 5.5 | 7 | 12 | 30 | 58 | 80 |

To find the regression model use Ti-83 calculator.

Step 1: Press ON tab and then click on STAT tab and then press ā1ā.

Step 2: Click on Edit and then put the value of time *t* in column *F* in

**(b)**

To determine

**To fill:** The missing quantity in the statement “According to the model, Facebook membership each year was ____ times that of the year before’

**(c)**

To determine

**To calculate:** The number of Facebook membership in early 2009 if the number of Facebook members at various times early in its history is shown by the provided table.

Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E

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