MATH102 December 2017
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 • Q9 (a) • Q9 (b) • Q9 (c) • Q10 (a) • Q10 (b) • Q10 (c) • Q10 (d) • Q11 (a) • Q11 (b) • Q12 (a) • Q12 (b) • Q12 (c) • Q12 (d) • Q13 (a) • Q13 (b) • Q13 (c) • Q13 (d) • Q14 (a) • Q14 (b) • Q15 (a) • Q15 (b) • Q16 •
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
that is, Let us first solve for . In fact, since , the first equation simplifies to Equating this with the second equation, we have Therefore, and
This is the value of .