- anonymous

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

- katieb

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- anonymous

Any ideas? IrishBoy :)

- anonymous

Before any plotting, let's create a table,
|dw:1438978318051:dw|

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- anonymous

Ok :) I see. Now what do we do?

- anonymous

take any numbers of values, then plot them on a graph
|dw:1438978459965:dw|

- anonymous

Oh! Cant we use graphing technology? Like fooplot.com?

- anonymous

That is something you would know, is this a question for school or what?If so you should ask your teacher if you can use a graph online

- anonymous

You can:)

- anonymous

Ok the question says either by hand or by technology, so you're free to use any online graphing softwares

- anonymous

I was just wondering, if you could just use graphing technology instead of drawing it to make it more clear

- anonymous

So what would the graph look like?

- anonymous

- anonymous

|dw:1438979039696:dw|
It would look something like this, search "graph -log(x)" on google and it will generate a graph for you

- anonymous

Alright thanks. Now what about this part?
2. 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.

- mathmate

First we will use the identity
\(\Large y=log_b x~~means~~ x=b^y\)
so if
\(p(t)=y=-log10(t)=log10(1/t)\)
then
\(1/t=10^y\)
or
\(t=10^{1/y}=10^{-y}\)
If\( y=0.5~~then~~ t=10^{-0.5}\)

- anonymous

|dw:1438979139010:dw|
Isn't it -log10(2)=-2??

- anonymous

Am I wrong?

- anonymous

\[p(t)=-\log(t)\]
If you shift your t by 0.5, your graph will also change, I don't see how you could use the same graph, you would need to shift it slightly\[p(t+0.5)=-\log(t+0.5)\]

- anonymous

yes you are wrong, what I mean by in that table is
\[-\log_{10}(2)=-0.3010\]

- anonymous

Last one!
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)

- mathmate

Check:
p(10^-0.5)=-log10(10^-0.5)=-(-0.5)=0.5

- mathmate

g(x)=f(x)+k will translate the graph of f(x) vertically (shifts up by k)
g(x)=f(x-h) will translate a graph of f(x) horizontally to the right by "h".
which implies g(x)=f(x+h) will translate graph of f(x) to the left by h.
g(x)=-f(x) will flip the graph about the x-axis.
So make your choice according to the requirements.

- anonymous

um the first one?

- anonymous

I dont understand how to graph #1?

- mathmate

You have already graphed p(t) at the very beginning.|dw:1438979941325:dw|
You will have to figure out which translation will result in a y-intercept!

- anonymous

ok so -log10(0)=0
-log10(1)=-1

- anonymous

I understand:) Whoops! Ok let's got back to #3 bcuz i dont understand that one

- anonymous

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)

- mathmate

no, log(1)=0 (to any base)
and log(0) does not exist.

- anonymous

oh! Sorry !!

- mathmate

Sorry, gtg, I'll continue later if no one gave you help in the mean time!

- anonymous

Thanks so much:)

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