Problem 1. A small bakery factory is collecting flour to have enough stock to begin operation at a later date. A storage silo is used to collect the flour. For now, no material is being removed from the silo, but a supplier has forecast that the rate at which flour can be provided to the factory will be given by = k exp (-k2t) where ky has units of lbm per day and k2 has units of 1/day. The silo initially holds a mass of M. lbm of flour. You are asked to determine the mass of flour expected to be in the silo after a sufficiently long time. First you will provide this mass as an algebraic expression, then you are asked to evaluate this expression for specific numerical values. Please make sure in addressing this prompt that you do the following: Clearly depict and explain an appropriate choice of system. Show the work necessary to get to the variable-separated part of your mathematical model, so that you can clearly communicate the bounds on your definite integrals. Show the work necessary from there to obtain the expression for the mass of flour in the silo for very long times (t = 0) only in terms of the variables and parameters defined above. Provide the numerical value for the long time mass if Mo = 1000, k, = 200, and k2 = 0.1 (in the same units as what is listed above)