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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.1, Problem 74E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Internet Users The rate of growth of the number of Internet users I (in billions) in the world from 2000 through 2014 can be modeled by

d I d t = − 0.000176 t 3 + 0.00243 t 2 + 0.0070 t + 0.092 where t is the time in years, with t = 0 corresponding to 2000. The number of Internet users in 2014 was 2.9 billion. (Source: International Telecommunication Union)

(a) Find the model for the number of Internet users in the world.

(b) Use the model to predict the number of Internet users in the world in 2018. Does your answer seem reasonable? Explain your reasoning.

(a)

To determine

To calculate: The model for the number of internet users in world whose rate of growth of the number of internet users I (in billions) in the world from 2000 through 2014 can be modeled as dIdt=−0.000176t3+0.00243t2+0.0070t+0.092 where t is the time in years, with t=0 corresponding to 2000.

Explanation

Given Information:

The provided model for rate of growth of the number of Internet users I (in billions) in the world from 2000 through 2014 is dIdt=−0.000176t3+0.00243t2+0.0070t+0.092 and the number of Internet users in 2014 was 2.9 billion where the corresponding time for year 2000 is t=0.

Formula used:

The sum rule of basic integration ∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx.

The simple power rule of integration ∫xndx=xn+1n+1+C.

Calculation:

Consider the provided model for rate of growth of the number of Internet users is dIdt=−0.000176t3+0.00243t2+0.0070t+0.092.

Integrate the provided model, use the sum rule of basic integration ∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx.

∫dIdtdt=∫(−0.000176t3+0.00243t2+0.0070t+0.092)dtM(t)=−0.000176∫t3dt+0.00243∫t2dt+0.0070∫tdt+∫0.092tdt

Integrate further, use the simple power rule of integration ∫xndx=xn+1n+1+C.

I(t)=−0.000176∫t3dt+0.00243∫t2dt+0

(b)

To determine

To calculate: The prediction of the number of Internet users in the world in year 2018 with reason.

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Statistics for Business & Economics, Revised (MindTap Course List)

Line PQ and RS are either parallel or perpendicular. Find x or y. Parallel: P(3,7);Q(2,9);R(10,4);S(x,6)

College Algebra (MindTap Course List)

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile rang...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Consider the following data on y = Number of songs stored on an MP3 player and x = Number of months the user ha...

Introduction To Statistics And Data Analysis

Divide the following terms as indicated. FS2FS2

Mathematics For Machine Technology

What is the primary threat to internal validity for a study that compares different groups of participants?

Research Methods for the Behavioral Sciences (MindTap Course List)

Define applied research and basic research and identify examples of each.

Research Methods for the Behavioral Sciences (MindTap Course List)

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