BENG 130 Lecture 14: Lecture 14
Document Summary
Lecture 14: the changes of x are much quicker than the production of y, so it is viable to, the rate of change of y depends on two things: synthesis of y and consumption. Rate of change of y: say we have some pathway where x y, the process, in (x,y) notation, is: (cid:4666)(cid:882),(cid:882)(cid:4667) (cid:4666),(cid:3046)(cid:3047)(cid:4667) assume that the time for the change of x is negligible. (cid:3046)(cid:3047) is the amount of y at steady state (doesn"t change) Is the rate of production of y of y. Is the rate of consumption of y, per unit (hence multiplication: (cid:2009)=(cid:2009)(cid:3031)(cid:3032)+(cid:2009)(cid:3031) (cid:2009)(cid:3031)(cid:3032) is the rate of degradation of y. (cid:2009)(cid:3031) is the rate of dilution/dissipation of y: (cid:1877)(cid:3046)(cid:3047) is the value of y where the change in y is 0 (so (cid:3031)(cid:3031)(cid:3047)=(cid:882)), so, using the differential form, we can solve: This function describes y at any given value of t. The maximum value (the asymptote) is =(cid:3046)(cid:3047)=(cid:3081)(cid:3080)
