The number of new prison admissions (into state or federal facilities) between 2
ID: 2886066 • Letter: T
Question
The number of new prison admissions (into state or federal facilities) between 2002 and 2011 is given by the function N(t) = 87.244444t3 2482.35t2 + 46009.26t + 579185 (2 t 11)
where t is measured in years, with t = 2 corresponding to 2002.† Show that the number of new prison admissions peaked in 2006 by finding the time t where N(t) has a maximum. Hint: Use the quadratic formula. (Round your answer to two decimal places.)
t =
What was N(t), the highest number of new inmates, at that time? (Round your answer to the nearest whole number.)
N(t) =
(This a practice problem, can you provide me the step by step process?) thanks
Explanation / Answer
N(t) = 87.244444t3 2482.35t2 + 46009.26t + 579185 given
N'(t)= -87.244*3*t^2-2482.35*2*t+46009.26=0 this gives
t=6.82
So maximum number of new prison admissions is N(6.82)=
87.244444*6.82^3 2482.35*6.82^2 + 46009.26*6.82+ 579185=749832.8897