Chapter 8.1, Problem 129E

a.

To determine

To find: a linear sequence and a quadratic sequence that model the given data and identify the coefficient of determination for each model.

Answer to Problem 129E

Linear sequence:

  $R_n=1573.16n-280.6,r^2\approx 0.9455$ .

Quadratic sequence:

  $R_n=253.00n^2-703.90n+4104.8,r^2\approx 0.9977$ .

Explanation of Solution

Given information: The revenue $R_n$ (in millions of dollars) of Netflix from 2012through

2017 are shown in the below table.

Year	Revenue, $R_n$ ( in millions of dollars)
2012	3609.3
2013	4374.6
2014	5504.7
2015	6779.5
2016	8830.7
2017	11,692.8

Calculation:

Let n =2 corresponding to 2012 then the above table will be:

Year	Revenue, $R_n$ ( in millions of dollars)
2	3609.3
3	4374.6
4	5504.7
5	6779.5
6	8830.7
7	11,692.8

Using the graphing calculator on the above table data.

Linear sequence:

  $R_n=1573.16n-280.6,r^2\approx 0.9455$ .

Quadratic sequence:

  $R_n=253.00n^2-703.90n+4104.8,r^2\approx 0.9977$ .

b.

To determine

To graph: each model with the data and decide which model is a better fit for the data.

Explanation of Solution

Given information:

Calculation:

The graph of each model is shown below.

  

The quadratic sequence is the better fit, because the coefficient of determination is close to 1.

c.

To determine

To predict: the revenue of Netflix in 2021 using the model in part (b).

Answer to Problem 129E

The revenue in 2021 is about $ 26,975.7 million.

Explanation of Solution

Given information:

Calculation:

Let n =11 for 2021

  $\begin{array}{l}{R}_{11}=253.007{(}^{11}-703.90(11)+4104.8\\ R_{11}\approx 26,975.7\end{array}$

Therefore, the revenue in 2021 is about $ 26,975.7 million.

d.

To determine

To find: when the revenue will reach 50 billion dollars using the modal from part (b).

Answer to Problem 129E

The revenue will reach $50 billion in 2024.

Explanation of Solution

Given information:

Calculation:

Let R =50,000.

  $\begin{array}{c}253,007n^2-703.90n+4104.8=50,000\\ 253,007n^2-703.90n-45,895.2=0\\ \text{Using}\text{the}\text{Quadratic}\text{Formula:}\\ n\approx 14.94\text{or}n=-\mathrm{12.16.}\end{array}$

Therefore, the revenue will reach $50 billion in 2024.

e.

To determine

To approximate: the total revenue from 2012 through 2017 and compare this sum with the result of adding the revenue shown in the table.

Answer to Problem 129E

The total revenue from 2012to 2017 is about $40,791.47 million. This sum is very close to the sum of the values shown in the above table data, which is $40,791.6 million.

Explanation of Solution

Given information:

Calculation:

The total revenue from 2012to 2017 is:

  $\begin{array}{l}{\displaystyle \sum _{n=2}^7(253.007n^2}-703.90n+4104.8)\\ \approx 3709.028+4270.163+5337.312+6910.475+8989.652+11,574.84\\ =40,\mathrm{791.47.}\end{array}$

Therefore, the total revenue from 2012to 2017 is about $40,791.47 million. This sum is very close to the sum of the values shown in the above table data, which is $40,791.6 million.