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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)=0.000176t3dt+0.00243t2dt+0.0070tdt+0.092tdt

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

I(t)=0.000176t3dt+0.00243t2dt+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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