Short calculations on the algae ponds.
a. If the pond is initially seeded with 0.5 mg/dm³ of algae, how long will it take the algae to reach a cell density (i.e., concentration) of 200 mg/dm³? Sketch a rough plot of r_g and C_C over time.
b. Suppose the algae limit the sun’s penetration significantly even before the concentration reaches 200 mg/dm³ by using μ = μ₀ (1 – C_C/200). Assume μ₀ = 0.9 day^–1. Qualitatively, what happens to the growth rate as the concentration of cells increases? Approximately how long would it take for the concentration to reach 200 mg/dm³? Why?
c. An invading algae species can double twice as fast as the strain you are cultivating. Assume that it is initially at a concentration of 0.01 mg/dm³. How long until it becomes the dominant species in the pond (over 50% of the cell density)?