Question

If you have ever swum in a pool and your eyes began to sting and turn red, you are aware of the effects on an incorrect pH level.
The pH level measures the concentration of hydronium ions and can be modeled by the function p(t) = –log10 t.
The variable t represents the amount of hydronium ions, and p(t) gives the resulting pH level.

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH lower than 7 is called acidic, while a pH above 7 is basic,
or alkaline. Seawater has a pH just over 8, while lemonade has a pH of approximately 3.

1.Create a graph of the pH function. Locate on your graph where the pH value is 0 and where it is. You may need to zoom in on your graph.

2. A pool company forgets to bring their logarithmic charts, but they need to raise the amount of hydronium ions in a pool by 0.50. Using complete sentences, explain how your graph can be used to solve 10–y = 0.50. Find the approximate solution.

3. The pool company has developed new chemicals that transform the pH scale. Using the pH function p(t) = –log10 t as the parent function, explain which transformation would result in a y-intercept. Use complete sentences and show all translations on your graph.

• p(t) + 1
• p(t + 1)
• –1 • p(t)

Answer 1

The question wants to solve the following base on the data in your problem and the answer are the following:
#1 The graph has the Y axis that is labeled as the value of p(t) and the x is the value of T. The graph that has a line that connect the A and B which is decreasing in the value of P(t) while increasing the value of T.
#2 It is the point in your graph that has the T value of 0.5 
#3 P(t+1) shifts all the values of p(t) to the left and allows to cross over the y axis