   Chapter 10.3, Problem 100E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Acquisition of Language The percentage q ( t ) ofchildren who can speak in sentences of five or more words by the age of t months can be approximated by the equation q ( t ) = 100 ( 1 − 5.27 × 10 17 t 12 )     ( t ≥ 30 ) . If p is the function referred to in the preceding exercise, Calculate lim x → + ∞ [ p ( t ) − q ( t ) ] , andinterpret the result. [HINT: See Example 4.]

To determine

To calculate: The value of limt+[p(t)q(t)], if the percentage of children who speak in sentences containing five or more words at an age of t months is provided as function:

q(t)=100(15.27×1017t12) (t30)

And the percentage of children who speak in at least single words at an age of t months is provided as function:

p(t)=100(112200t4.48) (t8.5)

Also, interpret the answer.

Explanation

Given Information:

The percentage of children who speak in sentences containing five or more words at an age of t months is provided as function:

q(t)=100(15.27×1017t12) (t30)

And the percentage of children who speak in at least single words at an age of t months is provided as function:

p(t)=100(112200t4.48) (t8.5)

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxaf(x) exists and f(a) is defined, then

limxaf(x)=f(a)

Calculation:

Consider the functions q(t)=100(15.27×1017t12), p(t)=100(112200t4.48)

Substitute the value in the limit limt+[p(t)q(t)].

limt+[p(t)q(t)]=limt+[100(112200t4

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