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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) = −log10x. 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. 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. Use your graph to find the ideal ph level if the amount of hydronium ions is raised to 0. 50. 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).

Sagot :

The pH level of a swimming pool indicates the level of acidity or alkalinity

of the swimming pool.

Correct Responses;

  • First Part:  Please find attached the required graph of the pH function created with MS Excel.
  • The pH value is 0 when x = 1
  • The pH value is 1 when x = 0.1
  • The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.

  • Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.

Method by which the above responses are obtained

First part

The given pH function is f(x) = -㏒₁₀x

Where;

x = The amount of hydronium ions

A substance with a pH < 7 is acidic

A substance with a pH > 7 is alkaline

A neutral solution has pH = 7

Water is a neutral solution

  • The graph of the pH function created with MS Excel is attached

The table of values of the graph is as follows;

[tex]\begin{tabular}{|c|c|c}\underline{x}& \underline{pH}\\1 \times 10^{-14}&14\\1 \times 10^{-13}&13\\1 \times 10^{-12}&12\\1 \times 10^{-11}&11\\1 \times 10^{-10}&10\\1 \times 10^{-9}&9 \\1 \times 10^{-8}&8\\1 \times 10^{-7}&7\\1 \times 10^{-6}&6\\1 \times 10^{-5}&5\\1 \times 10^{-4}&4\\1 \times 10^{-3}&3\\1 \times 10^{-2}&2\\1 \times 10^{-1}&1\\1 \times 10^0 = 1&0 \end{array}\right][/tex]

From the graph, we have;

  • When the pH value is 0, the hydronium ion concentration is 1

  • The pH value is 1 when x = 1 × 10⁻¹ = 0.1

The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;

pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996

  • The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996

Second Part

Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted

From the graph, we have;

The graph of f(x) + 1 = -㏒₁₀x + 1

The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)

At the y-intercept, x = 0, therefore;

f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined

f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0

Therefore;

  • The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.

Learn more about the pH here:

https://brainly.com/question/13280345

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