Based on data from the U.S. Census Bureau, the number of people (in millions) in the United States below the poverty level between 1999 (t = 0) and 2009 (t =10) can be approximated by the function

P(t) = - 0.0982t3+1.21t2 – 3.322t +34.596,
where t is the number of years since March 1999.

a.Find P ‘(t)
P ‘(t) = -3(0.0982t2) + 2(1.21t) - 3.322 = -.2946t2 + 2.42t - 3.322

b.Find P”(t)
P”(t) = -6(0.0982t) + 2(1.21) = -.5892t + 2.42

c.Complete the table below. (2 DECIMAL PLACES)

t P(t) P’(t) P “(t)
0
1
2
3
4
5
6
7
8
9
10

Question

Based on data from the U.S. Census Bureau, the number of people (in millions) in the United States below the poverty level between 1999 (t = 0) and 2009 (t =10) can be approximated by the function

P(t) =  - 0.0982t3+1.21t2 – 3.322t +34.596,
where t is the number of years since March 1999.

a.Find P ‘(t)
P ‘(t) = -3(0.0982t2) + 2(1.21t) - 3.322 = -.2946t2 + 2.42t - 3.322

b.Find  P”(t) 
P”(t) = -6(0.0982t) + 2(1.21) = -.5892t + 2.42

c.Complete the table below. (2 DECIMAL PLACES)

t	P(t)	P’(t)	P “(t)
0			
1			
2			
3			
4			
5			
6			
7			
8			
9			
10