Question

The BMV predicts that the index will be given by I (t) 0.06 -0.51 4-e Where t is the time in months and t= 0 corresponds to September 2019. (a) Determine the periods where the index will be growing and the periods where the index would be decreasing. (b) Calculate lim 1(t) and gives an interpretation. t-00

Answer 1

Vim 100) > eo plans Now, let po 4-ést Ilt) 0.06 4-60.5t Lim 16t)= 0.06 4-9560 8.06 M-ě ost 0.06 " -é:50) 0.06 = 0.015 14) 0.06 110 "- e 0.5(6) 0.06 0.06 -e 4-1 for the period where Ilt) is groning di(t) GE o 1 ost ap 6.06 -0.02 3 » (1(t)) = 0.06 # (Teost) = 0.064 (1 costa? (test (o ) reostos) &(-es) - spl) # == 006 o.st) 1 0.5 (4-posta

Now, dI -0.5t 0.63 e JE (4-6 ost 2 Here, denominator is always positine (square team) and numerater is always negative V since, post is always positive and -0.03(e-ost is mill be regative) 6 Flis cott (a) I(t) is strictly decreasing functions in for to (OP- Ilt) (0,0015) - >t (6) lim 0.06 lim too 110) = too 4.6-0.5t 0.06 Lim ta 006 4. 0.015 11 4-gostoso