   Chapter 3.3, Problem 93E

Chapter
Section
Textbook Problem

# Law Enforcement in the 1980s and 1990s The cost of fighting crime in the United States increased significantly during the period 1982–1999. Total spending on police and courts can 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 ) , respectively, where t is time in years since 1980. Compute lim t → + ∞ P ( t ) C ( t ) totwo decimal places, and intercept the result. [HINT: See Example 4.]

To determine

To calculate: The value of limx+P(t)C(t), if the total spending on police and courts in the United States is provided as a function of time as:

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

If it is given that the cost of fighting crime increased during 19821999 and also interpret the answer.

Explanation

Given Information:

The total spending on police and courts in the United States is provided as a function of time as:

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

The cost of fighting crime increased during 19821999.

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 2t19

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

limx+P(t)C(t)=limx+1

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