1. Population Growth Modeling

2. Begin with a mass balance on microbial growth X = population biomass, mg/L V = volume, L Q = flow, L/d k = 1 st order rate coefficient, 1/d t = time, d

3. (Mihelcic 1999, Figure 5.4) Exponential growth model when applied to growth rate calculations, the notation for the 1 st order rate coefficient (k) is replaced by , termed the specific growth rate coefficient.

4. Environmental Resistance (Mihelcic 1999, Figure 5.5)

5. Logistic growth model (Mihelcic 1999, Figure 5.7) K = carrying capacity, mg/L

6. Example: carry capacity effects (Mihelcic 1999, Figure 5.6)

7. Monod Model (Mihelcic 1999, Figure 5.8) Consider S,X = f (t) S = food, mg/L K s = half-saturation constant, mg/L Low values of K s indicate an ability to acquire food resources at low concentrations.

8. Example: resource competition (Mihelcic 1999, Figure 5.9)

9. The Yield Coefficient Y = yield coefficient, mgX/mgS Consider Y to be the amount of biomass produced per unit food consumed.

10. The Death (Respiration) Coefficient k d = death coefficient, 1/d It isn’t really death, a singular event, but rather losses of biomass to respiration.

11. Putting It All Together (Mihelcic 1999, Figure 5.10) These differential equations are solved using numerical methods.