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cowmoo32
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Homework Statement
Let S(t) represent the amount of a chemical reactant present at time t, where t>= 0. Assume that S(t) can be determined by solving the initial value problem
http://webwork.math.ncsu.edu/webwork2_files/tmp/equations/21/885ac2eff6f65b363662233870e25e1.png
where a, K, and S0 are positive constants. Obtain an implicit solution of the initial value problem. (The differential equation, often referred to as the Michaelis-Menten equation, arises in the study of biochemical reactions.)
The Attempt at a Solution
[itex]\frac{dS}{dt}[/itex] = [itex]\frac{aS}{K + S}[/itex]
[itex]\int[/itex][itex]\frac{K + S}{aS}[/itex] = [itex]\int[/itex]dt
ln(aS)([itex]\frac{S^2}{2}+KS[/itex]) = t
I'm not even sure how to begin to solve for S
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