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 pH's above 7 are basic or alkaline. Seawater has a pH just over 8, while lemonade has a pH of approximately 3.a. The pool maintenance man forgot to bring his logarithmic charts, and he needs to raisethe amount of hydronium ions, t, in the pool by 0 45. To do this, he can use the graph you createdUse your graph to find the pH level if the amount of hydronium ions is raised to0.45b. Then, convert the logarithmic function into an exponential function using y for the рН.

Answer 1

Given the equation that represents pH level.

The pH level measures the concentration of hydronium ions and can be modeled by the function p(t)

`p(t)=-log_(10)t`

The variable t represents the amount of hydronium ions, and p(t) gives the resulting pH level.

a. we will find pH when t = 0.45

so, substitute t = 0.45 and find the value of p

`pH=-log_(10)0.45=0.347`

b. We will convert the logarithmic function into an exponential function using y for the рН.

So, the process will be as follows:

`\begin{gathered} y=-log_(10)t \\ -y=log_(10)t \\ \\ 10^(-y)=t \\ \end{gathered}`

So, the answer will be, the equation will be as follows:

`t=10^(-y)`