The Internet is defined as a worldwide interconnection of individua...

  1. Home
  2. Homework Library
  3. Mathematics
  4. Calculus
  5. The Internet is defined as a worldwide interconnection of individua...


Transcribed TextTranscribed Text

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)=0.24x^2+4.12x+25.49 where x is the number of years from 1994. For the questions that require calculations, be sure to show your work details. If applicable, round your final answers to the nearest hundredth (2 digits after the decimal point) to receive full credit. For critical thinking questions, explain in detail how the answers were determined. Using integration on P'(x), find the function P(x) that predicts the number of Internet users in the world x years after 1994. (Note: Since this is an indefinite integral, do not forget to add a constant of integration, C, in your final answer.) Show your work details. 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. Show your work details. First letter of your last name x (years from 1994) 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 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. Using P(x), complete the following table. Show the work details for full credit. Year x Predicted Number of Internet Users P(x) (in millions) 2016 2018 2020 Below is a graph of P'(x) over the interval [6,22]. Set up the definite integral that will calculate the area of the shaded region on the graph. Calculate the area of the shaded region. Show your work details. What information does the area give in terms of number of Internet users in this scenario? Would you estimate that this is a reasonable growth of Internet users from 2000 to 2016? Explain and justify your answer with critical thinking.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Calculus Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats