Since its inception in 1971, socially responsible investments, or SRI\'s, have y
ID: 2875361 • Letter: S
Question
Since its inception in 1971, socially responsible investments, or SRI's, have yielded returns to investors on par with investments in general. The assets of socially responsible funds (in billions of dollars) from 1991 through 2001 is givem by
f(t) = 23.7 (0.2t + 1)^1.32
(0< or equal to t < or equal to 11)
where t = 0 corresponds to the beginning of 1991.
1. Find the rate of change (f '(t)) at which the assets of SRI's were changing.
2. Find the rate at which assets were changing at the beginning of 1994? 1999? 2002? Rounded to nearest tenth.
Explanation / Answer
given f(t) = 23.7 (0.2t + 1)1.32
1) rate of change f '(t)=23.7*1.32(0.2t + 1)1.32-1*(0.2*1 +0)
rate of change f '(t)=23.7*1.32(0.2t + 1)0.32*(0.2)
rate of change f '(t)=6.2568(0.2t + 1)0.32
2)at the beginning of 1994 , t =3
rate of change f '(3)=6.2568(0.2*3 + 1)0.32
rate of change f '(3)=7.3 billion dollars per year
at the beginning of 1999 , t =8
rate of change f '(8)=6.2568(0.2*8 + 1)0.32
rate of change f '(8)=8.5 billion dollars per year
at the beginning of 2002 , t =11
rate of change f '(11)=6.2568(0.2*11 + 1)0.32
rate of change f '(11)=9.1 billion dollars per year