The shelf life, in days, for bottles of a certain prescribed medicine

ASSIGNMENT :

[NOTE:  The assignment is to be done entirely BY HAND]

1.   The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function

a)  Find the value of A. 

b)  Find the probability that a bottle of this medicine will have a shelf life of anywhere from 80 to 120 days. 

c)  Find the average shelf life. 

2.     Consider the logistic equation (section 9.5) which is an equation of the form

   ( constants).  (1)

       First separate the variables in Eq. (1) and then derive the solution    

                                              (2)

      that satisfies the initial condition .  If  and are positive 

        constants, then .  Hence then parameter  in (1) is the limiting

         population.