Question

If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, 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.

Answer 1

`pH = 0` when
`t = 1`

`pH = 1` when
`t = 0.10`

Explanation:

The graph of
`y = p(t)` is shown in the image.

The vertical axis represents the values ​​of t

The horizontal axis represents the pH values ​​as a function of t.

We want to know when the pH value is 0 and when it is equal to 1. then we look in the graph for the cut point of the graph with the horizontal axis. For that value the pH will be 0.

In the graph, note that
`pH = 0` when
`t = 1`.

Then we look in the graph for the point in the curve for which
`y = p(t)=1`

Note that this point is
`t = 0.1`
`p(t) = 1`