Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 02
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Question B 02 

A population of zebra mussels, an invasive species now found in many rivers in North America, grows at a rate proportional to the current population level starting from . The constant of proportionality is per year. After how many years will ? 
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 

The question is describing the linear differential equation . 
Hint 2 

The solution to the linear differential equation has form , where is the initial condition and is the growth rate. 
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. According to given information, we write down the equation describing the rate of change of the mussel population as where is a constant. Solving it we obtain With and , it becomes When , solving for we get and hence . 