Discussion Post Unit 3 - Selection of my best coursework PDF

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Selection of my best coursework...

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Discussion Post Unit 3 Real-life applications of rational functions in everyday life Polynomial and rational functions can indeed be used to model a wide variety of phenomena of science, technology, and everyday life. They can be utilized in math to compute real-world scenarios. For example, polynomials are used in images when they are opened. The photo editing software uses these calculations for methods of cropping and transforming images as needed. Polynomial equations are usually a statement that raises the equality of two expressions, where a given term that makes up each side of the equality are polynomials (Abramson, 2017 p. 364). Here is an example in Science from Exercise 80, (Abramson, 2017, p. 434). A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 10 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after t minutes. Solution: Let water be: W(t) = 200 + 10t in gallons Let sugar be: S(t) = 10 + 3t in pounds The concentration C, will be the ratio of pounds of sugar to gallons of water C(t) = S(t) / W(t) = (10 + 3t) / (200 + 10t) = (10 + 3t) / (200 + 10t) Therefore C(t) = (10 + 3t) / (200 + 10t) The concentration started at zero: t=0 C(t) = (10 + 3t) / (200 + 10t) C(5) = (10 + 3(0)) / (200 + 10(0)) = (10 + 0) / (200 + 0) = 10/200 = 1/20 or 0.05 This means that the concentration at the beginning is 1 pound of sugar to 20 gallons of water. Now let us check the concentration after 20 minutes: t = 20 C(t) = (10 + 3t) / (200 + 10t) C(5) = (10 + 3(20)) / (200 + 10(20)) = (10 + 60) / (200 + 200) = 70/400 = 7/40 or 0.175 This means that the concentration is 7 pounds of sugar to 40 gallons of water. Since the concentration was 0.05 at the beginning and becomes 0.175 later, we can simply conclude that the concentration is increasing because 0.175 > 0.05. Here is a graph:

Reference: Abramson, J. (2017). Algebra and Trigonometry. OpenStax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry....