Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (c)
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Question C 02 (c) 

The graphs to the right show two functions,
where , and . Suppose that is the concentration of a substance involved in a chemical reaction and satisfies the equation If the concentration is initially , what concentration does eventually approach? 
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? 
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Hint 

Is the derivative positive or negative at ? Will the function increase or decrease after ? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Observe that according to the graph. Therefore, is positive initially, so that would increase with time. On the other hand, the value falls in the interval , i.e., . Remember that when the graphs of and intersect, we have . In other words, the steady states are obtained at the intersection points. In the graph, when we start from and move to the right (because it increases with time), the first steady state that we meet is . Therefore, approaches the steady state . Answer: 