The following is used for all problems 1-6 below: A scientist adds 60 ml of pure water and 15 ml of acid to a beaker, creating a 20% acid solution. 1. Explain/show how this 20% value is calculated. 2. Explain/show how adding an additional 45 ml of pure water will give you a 12.5% acid solution. 3. Model the scenario above, where the concentration of acid is a function of the amount of water added. Hint: This should a rational function.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.2: Linear Functions And Applications
Problem 23PS
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The following is used for all problems 1-6 below: A scientist adds 60 mL of pure water and 15
ml of acid to a beaker, creating a 20% acid solution.
1. Explain/show how this 20% value is calculated.
2. Explain/show how adding an additional 45 ml of pure water will give you a 12.5% acid
solution.
3. Model the scenario above, where the concentration of acid is a function of the amount of
water added. Hint: This should a rational function.
4. Discuss practical aspects of your function and what they mean in this context:
a. Domain
b. Range
c. When is your function Increasing, decreasing, constant?
d. Vertical and horizontal asymptotes
5. How many ml of water must be added to obtain a
_% solution? (you picka
percentage, but your solution should include algebra)
6. Discuss the inverse of your function
a. Find and name your inverse function using reasonable notation.
b. What are the practical domain and range of your inverse function?
c. Discuss how your inverse can be used. In other words, what would be the
purpose of using your inverse function? Give an example using your inverse and
explain it using the context.
Transcribed Image Text:The following is used for all problems 1-6 below: A scientist adds 60 mL of pure water and 15 ml of acid to a beaker, creating a 20% acid solution. 1. Explain/show how this 20% value is calculated. 2. Explain/show how adding an additional 45 ml of pure water will give you a 12.5% acid solution. 3. Model the scenario above, where the concentration of acid is a function of the amount of water added. Hint: This should a rational function. 4. Discuss practical aspects of your function and what they mean in this context: a. Domain b. Range c. When is your function Increasing, decreasing, constant? d. Vertical and horizontal asymptotes 5. How many ml of water must be added to obtain a _% solution? (you picka percentage, but your solution should include algebra) 6. Discuss the inverse of your function a. Find and name your inverse function using reasonable notation. b. What are the practical domain and range of your inverse function? c. Discuss how your inverse can be used. In other words, what would be the purpose of using your inverse function? Give an example using your inverse and explain it using the context.
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