Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (c)
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Question 13 (c)
A biochemical reaction in which a substance is both produced and consumed is described by the differential equation
where denotes the concentration of the substance, is a constant and the units are omitted.
(c) For what positive value of is the line tangent to ? Call this value .
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We look for an intersection point other than the origin.
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we differentiate using the power rule and chain rule to yield
At the point (which is not the origin) where is tangent to , we have
Let us first solve for . In fact, since , the first equation simplifies to
Equating this with the second equation, we have
This is the value of .