Science:Math Exam Resources/Courses/MATH101/April 2009/Question 08 (b)

MATH101 April 2009
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Question 08 (b)

Consider the chemical reaction

${\displaystyle \displaystyle A+B\rightarrow C+D.}$

Suppose at time t = 0 sec the concentration of chemical A is 0.1 mol/L, the concentration of chemical B is 0.2 mol/L, and the concentrations of chemicals C and D are both 0. For t ≥ 0, let x(t) be the concentration of chemical D in mol/L. It can be shown that x(t) is the solution to the initial-value problem

${\displaystyle {\frac {dx}{dt}}=k(0.1-x)(0.2-x),\quad x(0)=0,}$

where k is a positive constant whole value can be determined by experiment.

(b) What value does the concentration of chemical D approach as t approaches ${\displaystyle \infty }$?
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