Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right. pH is a measurement of hydronium ions and can be modeled by the function f(x) = -log1ox. The variable x represents the amount of hydronium ions, and f(x) gives the pH level. Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3. 1. Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph. 2. Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50. 3. The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = -log10x as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the graph. • f(x) + 1 • f(x + 1)
Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right. pH is a measurement of hydronium ions and can be modeled by the function f(x) = -log1ox. The variable x represents the amount of hydronium ions, and f(x) gives the pH level. Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3. 1. Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph. 2. Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50. 3. The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = -log10x as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the graph. • f(x) + 1 • f(x + 1)
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Transcribed Image Text:Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More
specifically, the measurement of the pool's pH was not quite right.
pH is a measurement of hydronium ions and can be modeled by the function f(x) = -log1ox. The variable x represents the amount of hydronium ions, and f(x)
gives the pH level.
Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a
pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
1. Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may
need to zoom in on your graph.
2. Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50.
3. The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = -log10x as the parent function, explain
which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the
graph.
• f(x) + 1
• f(x + 1)
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