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(5) The Michaelis-Menten model describes the kinetics of enzyme mediated reactions: ds S V. kus dt where S = substrate concentration (moles/L), Vm = maximum uptake rate (moles/L/d), and ks = the half- saturation constant, which is the substrate level at which uptake is half of the maximum [moles/L]. If the initial substrate level at t = 0 is So, this differential equation can be solved for S = S, vt+k, In(S, /S) f(S)= So - Vt+ k In (S. /S)-S Determining the root of f(S) where So = 8 moles/L, Vm= 0.7 moles/L/d, and ks = 2.5 moles/L. Iterate until 8 al