Science:Math Exam Resources/Courses/MATH103/April 2014/Question 05 (c)
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Question 05 (c) 

A mutation occurs within a bacterial species that allows it to acquire antibiotic resistance. Through natural selection the abundance of the mutant trait increases in the population. Let be the fraction (i. e. ) of the population, which carries the antibiotic resistance trait. Suppose satisfies the following differential equation:
where is time (years). In the same situation as part (b), how long after does it take until of the bacterial population is resistant to antibiotics? Work must be shown for full marks. Simplify fully. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

What do and represent in this question? 
Hint 2 

Solve for . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The problem amounts to solving the equation for . Since we found in (b) that ,
