Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (c)
• 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 . 
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 

We look for an intersection point other than the origin. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. From 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 .
Answer: . 