Question

Pre-Cal :)))

Answer 1

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 2

does
p(t) = −log10t.
mean
\[ p(t)= - \log_{10} t \]
or
\[ p(t) = −\log(10t)\]?

Answer 3

The 1st one lol!

Answer 4

ok, I just googled it. Yes the first way.
\[ p(t)= - \log_{10} t \]

pick some values for t. I would pick powers of 10 (because it is easy to "take the log" )
thus let t= 0.001 (i.e. t= 10^-3
t= 0.01, or t= 10^-2
t= 0.1 or t= 10^-1
t= 1, t= 10^0
t=10 , t= 10^1

Answer 5

Ok, then how would u graph it?

Answer 6

first, what is the log of 10^-3 ?
\[ \log_{10} \left(10^{-3} \right) = \]

Answer 7

0.001?

Answer 8

10^-3 is 0.001
the log of 0.001 is the exponent (assuming we use base 10)
in other words
\[ \log_{10}(0.001) = \log_{10}\left( 10^{-3}\right) \]
what is the exponent ?

Answer 9

-3

Answer 10

ok.

\[ p(t)= - \log_{10} t \\= -1 \cdot \log(0.001) \\= -1 \cdot -3 = 3 \]

Answer 11

so
(0.001, 3) is a point on the graph
hopefully you can figure out the following points
(0.01,2)
(0.1, 1)
(1,0)
(10,-1)
(100,-2)
(1000,-3)

Answer 12

yes, I think I can. How could I graph this using technology?

Answer 13

if you have geogebra , you type in the equation

Answer 14

I dont have that/ know what that is lol :)

Answer 15

I have desmos.com but I wouldnt know how to type that in

Answer 16

Anyways, I'll figure it out:) No worries!! This is the 2nd 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.

Answer 17

just type in
y= -log(x)

Answer 18

oH! Hahaha thanks :)

Answer 19

What about the 2nd part of the question?

Answer 20

zoom in on your graph, and click on the curve when it has y=0.5
what do you get for the x value ?

Answer 21

I got (0.316,0.5)

Answer 22

for
** convert the logarithmic function into an exponential function using y for the pH.***
y= - log(t)
or, after multiplying by -1 on both sides:
-y = log(t)
now make each side the exponent of 10
\[ 10^{-y} = 10^{\log t} \]
the right side becomes t
\[ 10^{-y} = t \\ t= 10^{-y} \]

Answer 23

yes, 0.316 is good
using the exponential equation
\[ t= 10^{-0.5} = \frac{1}{\sqrt{10}} = 0.316228\]

Answer 24

So, we just converted it right? And that would be the answer to the question?

Answer 25

yes, the work to find the exponential form is up above.
and I used it to check your answer... and as you see we get the same number (rounded of course)

Answer 26

Yes! Thanks so much<3