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

Consider the chemical reaction 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 initialvalue problem where k is a positive constant whole value can be determined by experiment.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Use the previous part to get the equation. Then take the limit. You may want to factor out a from the numerator and denominator. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From the previous part, we know that
taking the limit as t tends to infinity yields
Thus, the concentration tends to as t tends to infinity. 