MATH102 December 2014
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QB 1 • QB 2 • QB 3 • QB 4 • QB 5 • QB 6 • QB 7 • QC 1 • QC 2(a) • QC 2(b) • QC 2(c) • QC 2(d) • QC 3 •
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?
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Is the derivative positive or negative at ? Will the function increase or decrease after ?
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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 .
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