1. Equilibrium

3. Stable equilibrium (negative feedback)

4. Unstable equilibrium (positive feedback),

5. At Equilibrium: Inflows=Outflows

6. 80 gal/min 120 gal ???

7. Assume Equilibrium: Inflows=Outflows 80 gal/min 120 gal 80 gal/min

8. At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 20 gal/min Is water level a)rising b)Falling c)Staying the same

9. At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 20 gal/min Is water level a)rising b)Falling c)Staying the same

10. At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 80 gal/min Is water level a)rising b)Falling c)Staying the same

11. At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 80 gal/min Is water level a)rising b)Falling c)Staying the same

12. At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 140 gal/min Is water level a)rising b)Falling c)Staying the same

13. At Equilibrium: Inflows=Outflows 80 gal/min 120 gal 140 gal/min Is water level a)rising b)Falling c)Staying the same

14. At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 20 gal ??=_________

15. At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 20 gal ??=_10 gal/min________

16. At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 16 gal ??=_________

17. At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 16 gal ??=__8 gal/min_______

18. At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 12 gal ??=_________

19. At Equilibrium: Inflows=Outflows Is water level a)rising b)Falling c)Staying the same =2 min 8 gal/min 12 gal ??=___6 gal/min_____

20. At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr 12 ppm =.2 (1/yr) ??=_________

21. At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr 12 ppm =.2 (1/yr) ??=__2.4 ppm/yr____

22. At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr ?? =.2 (1/yr) 8 ppm/yr What is the lifetime?

23. At Equilibrium: Inflows=Outflows Is pollutant level a)rising b)Falling c)Staying the same 8 ppm/yr ??= 40 ppm =.2 (1/yr) 8 ppm/yr What is the lifetime? Lifetime=1/(DecayConstant)=5 yr

24. Whenever the net flow = -k*stock you get exponential decay to zero** Summary (exponential decay/Goal seeking) Sometimes we like to use the concept of lifetime (decay time constant) instead of decay rate constant. Here k is the decay rate constant.

25. Whenever the net flow = inflow-k*stock you get exponential decay to a Goal, Xeq Summary (exponential decay/Goal seeking) The Goal is the value of X (the stock) that makes the net flow zero Inflow=outflow Inflow=k*stock at equilibrium Here X is any stock.

26. Ceq=Inflow*lifetime Ceq=Inflow/(DecayRateConstant) Outflow=Content/(lifetime) Outflow=DecayRateConstant*Content Summary (exponential decay/Goal seeking)