Chapter 3.3, Problem 93E

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

Chapter
Section

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
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+29.84Â ifÂ 2â‰¤tâ‰¤19C(t)=1.097t+10.65Â ifÂ 2â‰¤tâ‰¤19

The cost of fighting crime increased during 1982âˆ’1999.

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxâ†’af(x) exists and f(a) is defined, then

limxâ†’af(x)=f(a)

Calculation:

Consider the functions:

P(t)=1.745t+29.84Â ifÂ 2â‰¤tâ‰¤19C(t)=1.097t+10.65Â ifÂ 2â‰¤tâ‰¤19

Substitute the values in the limit limxâ†’+âˆžP(t)C(t). So,

limxâ†’+âˆžP(t)C(t)=limxâ†’+âˆž1

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