### Calculate the area of the shaded region

Assignment Help Mathematics
##### Reference no: EM131069776

Assignment-

The Internet is defined as a worldwide interconnection of individual networks operated by governments, industries, academia, and private parties (Internet World Stats, 2015).As the Internet grows and becomes more accessible to many people in the world, there is an increasing interest in forecasting its number of users as it helps improve the technology and its security.

In a recent study, researchers found that the rate of change of internet users in the world (in millions) is modeled by the function

P'(x) = 0.7338x2 + 3.1564x + 49.178

where x is the number of years from 1994.

For the questions that require calculations, be sure to show your work details and if applicable, round your final answers to the nearest hundredths (2 digits after the decimal point) to receive full credit. For critical thinking questions, explain in detail how the answers were determined.

1. Using integration on P'(x), find the function P(x) that predicts the number of internet users in the world. (Note: Since this is an indefinite integral, do not forget to add a constant C in your final answer.)

2. Based on the first letter of your last name, calculate the value of C from #1 by choosing an ordered pair (x, P(x)) from the table below.

 First letter of your last name x P(x) (in millions) A-B 6 361 C-D 7 513 E-F 8 587 G-H 9 719 I-J 10 817 K-L 11 1,018 M-N 12 1,093 O-P 13 1,319 Q-R 14 1,574 S-T 15 1,802 U-V 16 2,267 W-X 17 2,497 Y-Z 18 2,802

3. From your answers in #1 and #2, state the mathematical model, P(x) (in millions), that will predict the number of internet users in the world.

4. Using P(x), complete the following table.

 Year x Predicted Number of Internet Users (in millions) 2016 2018 2020

5. Below is a graph of P'(x)over the interval [2, 10]. Set up the definite integral that will calculate the area of the shaded region on the graph.

6. Calculate the area of the shaded region.

7. Interpret what the area means in terms of the given scenario.

8. As the Internet grows and becomes more accessible to many users, what do you think are its advantages and disadvantages? Be thorough in your explanation and if necessary to support analysis, be sure to include your reference/s in APA format.

References-

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