Science:Math Exam Resources/Courses/MATH110/December 2015/Question 10 (a)
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Question 10 (a)  

Upon the first snow fall of the year, your friends in Ontario always place a metre stick in their yard so they can measure how much snow they get throughout the winter. Their measurements for last year’s snow during the month of December are shown in the table below.
(a) According to the table, what is the minimum number of times your friends must have had exactly 20 cm of snow in their yard? Justify your answer. 
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 

Use the Intermediate Value Theorem. 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let's first recall the statement of the Intermediate Value Theorem: If is a continuous function on the interval and is a number between and , then there must be a number in the interval such that . Now we apply IVT in the context of the given problem. First, we note that since the metre stick is always placed in the yard, so it is continuously measuring the height of snow, this means that the function of height, , is a continuous function in the interval of the days in December i.e. . The target value cm is between cm and cm, so we know that at least there is one day say th day such that the amount of snow has been cm. However, if we look closely to the given table we see that we can split the interval into smaller subintervals such that for each subinterval, the number is between and :
