Answer:
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
