#### Transcript of 07.07 Graphing Logarithmic Functions

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.

Question 1

Question 2

Question 3

Original function is p(t) = -log10t which is the Red line

Parent(Red): y=-log(t)

Graph 1(Blue): y=-log(t)+1

Graph 2(Green):y=-log(t+1)

Graph 3(Purple):y=-1x-log(t)

Steps

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.

The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool by 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.

The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.

p(t) + 1

p(t + 1)

−1 • p(t)

**07.07 Graphing Logarithmic Functions**

**By Darion Jean**

On the graph 1 is where the pH=0 and 0.5 is where the pH equals 1

Equation used: y=-logt

What I need to get is 10^-y = 0.50 from y=-log10t then just multiply both sides by -1 and so on and Ill get Y=0.4 and t= 0.50

On the graph 1 is where the pH=0 and 0.5 is where the pH equals 1

Original function is p(t) = -log10t which is the Red line

Parent(Red): y=-log(t)

Graph 1(Blue): y=-log(t)+1

Graph 2(Green):y=-log(t+1)

Graph 3(Purple):y=-1x-log(t)

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