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The concentration (C) of a given substance in a mixture is the ratio of the amount of substance to the total quantity. In symbols, C = S where C is the concentration, S is the amount of substance, and T is the total quantity. If 8 ounces of punch contains 4 ounces of pure orange juice, the concentration of orange juice in the punch is 4/8 or 50%. The punch is 50% orange juice. Consider the problem where we begin that 8 ounces of punch that is 50% orange juice and want to write a function that gives the orange juice concentration after x ounces of pure orange juice are added. Questions: 1. How much orange juice do you begin with? Write an expression for the amount of orange juice present after x ounces has been added. 2. Write an expression for the total amount of punch present after x ounces has been added. 3. Using the answers in (a) and (b), write a rational function defining the pineapple juice concentration as a function of x. 4. Give the x and y - intercepts of the rational function. 5. What is the equation of the vertical asymptote and of the horizontal asymptote?

The concentration (C) of a given substance in a mixture is the ratio of the amount of substance to the total quantity. In symbols, C = S where C is the concentration, S is the amount of substance, and T is the total quantity. If 8 ounces of punch contains 4 ounces of pure orange juice, the concentration of orange juice in the punch is 4/8 or 50%. The punch is 50% orange juice. Consider the problem where we begin that 8 ounces of punch that is 50% orange juice and want to write a function that gives the orange juice concentration after x ounces of pure orange juice are added. Questions: 1. How much orange juice do you begin with? Write an expression for the amount of orange juice present after x ounces has been added. 2. Write an expression for the total amount of punch present after x ounces has been added. 3. Using the answers in (a) and (b), write a rational function defining the pineapple juice concentration as a function of x. 4. Give the x and y - intercepts of the rational function. 5. What is the equation of the vertical asymptote and of the horizontal asymptote?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The concentration (C) of a given substance in a mixture is the ratio of the amount of substance to the total quantity. In symbols, C = S Q where C is the concentration, S is the amount of substance, and T is the total quantity. If 8 ounces of punch contains 4 ounces of pure orange juice, the concentration of orange juice in the punch is 4/8 or 50%. The punch is 50% orange juice. Consider the problem where we begin that 8 ounces of punch that is 50% orange juice and want to write a function that gives the orange juice concentration after x ounces of pure orange juice are added. Questions: 1. How much orange juice do you begin with? Write an expression for the amount of orange juice present after x ounces has been added. 2. Write an expression for the total amount of punch present after x ounces has been added. 3. Using the answers in (a) and (b), write a rational function defining the pineapple juice concentration as a function of x. 4. Give the x and y - intercepts of the rational function. 5. What is the equation of the vertical asymptote and of the horizontal asymptote?
Transcribed Image Text:The concentration (C) of a given substance in a mixture is the ratio of the amount of substance to the total quantity. In symbols, C = S Q where C is the concentration, S is the amount of substance, and T is the total quantity. If 8 ounces of punch contains 4 ounces of pure orange juice, the concentration of orange juice in the punch is 4/8 or 50%. The punch is 50% orange juice. Consider the problem where we begin that 8 ounces of punch that is 50% orange juice and want to write a function that gives the orange juice concentration after x ounces of pure orange juice are added. Questions: 1. How much orange juice do you begin with? Write an expression for the amount of orange juice present after x ounces has been added. 2. Write an expression for the total amount of punch present after x ounces has been added. 3. Using the answers in (a) and (b), write a rational function defining the pineapple juice concentration as a function of x. 4. Give the x and y - intercepts of the rational function. 5. What is the equation of the vertical asymptote and of the horizontal asymptote?
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