Science:Math Exam Resources/Courses/MATH103/April 2014/Question 05 (b)
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[hide]Question 05 (b) |
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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). At time it is determined that half of the bacterial population carries the antibiotic resistance trait. Determine the fraction of the bacterial population with antibiotic resistance as a function of time . Work must be shown for full marks. Simplify fully. |
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[show]Hint 2 |
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[show]Solution |
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