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)?

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 u₀ (1-C_C/200). Assume u₀ = 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)?

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