The cost of fighting crime in a country increased significantly during the period 1982-1999. Total spending on police, courts, and prisons in the period 1982-1999 could be approximated, respectively, by

P (t) = 1.743t + 29.84 billion dollars (2 ≤ t ≤ 19)

C (t) = 1.096t + 10.65 billion dollars (2 ≤ t ≤ 19)

J (t) = 1.917t + 12.36 billion dollars (2 ≤ t ≤ 19)

where t is time in years since 1980.

Compute lim t→+[infinity]

P (t)

P (t) + C (t) + J (t)

t→+[infinity] [ P (t) ] = $62.957 billion

t→+[infinity] [ f (t) ] = $143.214 billion

Step-by-step explanation:

Given:

- Total spending on police, courts, and prisons in the period 1982-1999 could be approximated, respectively,

P (t) = 1.743*t + 29.84 billion dollars (2 ≤ t ≤ 19)

C (t) = 1.096*t + 10.65 billion dollars (2 ≤ t ≤ 19)

J (t) = 1.917*t + 12.36 billion dollars (2 ≤ t ≤ 19)

Find:

- Compute lim t→+[infinity] for:

P (t) and P (t) + C (t) + J (t)

Solution:

- The limit as t→+[infinity] for the above three function can be accounted for by considering the domain of each function.

- All functions : P (t), C (t), J (t) have the domain 2 ≤ t ≤ 19:

- So in other words, lim t→+[infinity] = lim t→19

- The limits are as follows:

lim t→19 [ P (19) ] = 1.743*19 + 29.84 = $62.957 billion

- The function f (t) is as follows:

f (t) = P (t) + C (t) + J (t) = 4.756*t + 52.85 billion dollars

lim t→19 [ f (19) ] = 4.756*19 + 52.85 = $143.214 billion