   Chapter 10.3, Problem 94E 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

Law Enforcement in the 1980s and 1990s Refer to Exercise 93. Total spending on police, courts, and prisons in the period 1982–1999 could be approximated by P ( t ) = 1.745 t + 29.84  billon dollars     ( 2 ≤ t ≤ 19 ) C ( t ) = 1.097 t + 10.65  billon dollars     ( 2 ≤ t ≤ 19 ) , J ( t ) = 1.919 t + 12.36  billon dollars     ( 2 ≤ t ≤ 19 ) respectively, where t is time in years since 1980. Compute lim t → + ∞ P ( t ) P ( t ) + C ( t ) + J ( t ) totwo decimal places, and intercept the result. [HINT: See Example 4.]

To determine

To calculate: The value of limx+P(t)P(t)+C(t)+J(t), if the total spending on police, courts and prisons during the period 19821999 is approximated as functions of time as:

P(t)=1.745t+29.84 if 2t19C(t)=1.097t+10.65 if 2t19J(t)=1.919t+12.36 if 2t19

Also, interpret the answer.

Explanation

Given Information:

The total spending on police, courts and prisons during the period 19821999 is approximated as functions of time as:

P(t)=1.745t+29.84 if 2t19C(t)=1.097t+10.65 if 2t19J(t)=1.919t+12.36 if 2t19

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:

P(t)=1.745t+29.84 if 2t19C(t)=1.097t+10.65 if 2t19J(t)=1.919t+12.36 if 2t19

Substitute the values in the limit limx+P(t)P(t)+C(t)+J(t). So,

limx+P(t)P(t)+C(t)+J(t)=limx+1.745t+29.84(1.745t+29.84)+(1.097t+10.65)+(1.919t+12.36)

Further simplify as:

limx+1.745t+29.84(1

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