ALGEBRAIC AND GRAPHICAL MODELLING Evaluation

MTH-3051-2 – ALGEBRAIC AND GRAPHICAL MODELLING Evaluation Situation 2 – Bye-Bye, Bacteria! A Montréal-based company wants to assess the effectiveness of two antibacterial sprays. In its lab, both products are sprayed on two similar-sized pieces of fabric containing the same number of bacteria. The company decides that the product that eliminates more bacteria as a function of the same spray time will be deemed more effective. Air Breeze To study the effectiveness of the Air Breeze antibacterial brand, the company’s biologist models its behaviour with a mathematical function representing the number of bacteria remaining per square decimetre as a function of spraying time. The table of values below shows the data extracted from this functional model. Number of Bacteria Remaining per as a Function of Spraying Time for Square Decimetre Air Breeze Brand Spraying time (s) 8 16 24 32 40 Number of bacteria remaining 480 240 160 120 96 No More Bacteria The biologist repeats the same tests to study the behaviour of the No More Bacteria antibacterial brand. She runs out of time to model its behaviour with a mathematical function. She has only recorded the results of the experiment in the following table of values. Number of Bacteria Remaining per Square Decimetre Function of Spraying Time for No More Bacteria Brand as a Spraying time (s) 5 10 15 20 25 30 35 45 55 Number of bacteria remaining 696 360 250 176 142 120 105 75 70 This company has recently hired you to assist the biologist. In the lab, you spray a piece of fabric measuring one square decimetre with the No More Bacteria antibacterial brand. You stop spraying when the number of bacteria remaining is at 200 per square decimetre. You must complete the analysis. 16 © SOFAD SCORED ACTIVITY 1 Task 1 You must calculate how many bacteria would remain on a piece of fabric of the same size if sprayed with the Air Breeze antibacterial brand for the same amount of time (s). Score for each criterion Cr. 1.1 5 4 3 2 1 Cr. 2.1 5 4 3 2 1 Cr. 2.2 10 8 6 4 2 Answer: /20 points © SOFAD 17 MTH-3051-2 – ALGEBRAIC AND GRAPHICAL MODELLING Task 2 The company wants to market the more effective product. The biologist asks you to determine which antibacterial spray is better, having studied the overall behaviour of both every five seconds. You must justify your choice using mathematical arguments related to the context. Answer: Score for each criterion Cr. 2.3 Cr. 2.4 10 10 8 8 6 6 4 4 2 2 /20 points Total for Part 2 18 /80 © SOFAD
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