Differential Equation (Application)

The rate at which enzyme A is converted to enzyme B is governed by the differential equation \displaystyle \frac{dq}{dt}=k\left(a-q\right)\left(b+q\right) where q denotes the concentration of enzyme B produced after t hours.

Here a and b are the initial concentrations of enzyme A and enzyme B respectively, while k is a positive constant.  If the initial concentrations, a and b, respectively, are 100 and 5 moles/litre, find the equation giving the concentration of enzyme B produced in the reaction after t hours when the concentration of enzyme B produced in the first hour is 10 moles/litre.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 6, p. 132)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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