Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 06

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MATH100 B December 2024

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Question 06

Let $M$ be the average size of a mosquito larva in a particular area. Let $x$ be the average rainfall in that area. Suppose it is observed that $M$ can be modelled as a function of $x$. Of the scenarios below, which is the most appropriate interpretation of $M^{\prime }(x)>0?$ Write the letter here:_______ For this question, you do not need to justify your answers. A. The rate of change of larva population is proportional to the population size. B. The number of larvae is increasing over time. C. The number of larvae is decreasing over time. D. The average size of mosquito larvae is increasing over time. E. The average size of mosquito larvae is decreasing over time. F. Heavy rain brings nutrients, which helps the larvae to grow large. G. Drier conditions kill off competitors, making it easier for the larvae to feed and grow large. H. Heavy rain disturbs the mosquitos’ breeding grounds, leading to larvae that are sickly and small.

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
Given that $x$ is rainfall and $M$ is the average size of a mosquito larva, the correct interpretation should involve both of these quantities. What does the statement $M^{\prime }(x)>0$ suggest about the relationship between these two quantities?

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. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution

In the problem we are given that the verge size of a mosquito larva in a particular area as a function of average rainfall in that area, i.e., $M(x)$. Then $M^{\prime }(x)$, represents the rate of change of larva size with respect to rainfall. Positive derivative means larvae size increases as rainfall increases. Thus, the correct interpretation is: H: Heavy rain brings nutrients, which helps the larvae to grow large

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