Question

A pool company forgets to bring their logarithmic charts, but they need to raise the amount of hydronium ions in a pool by 0.50. Using complete sentences, explain how your graph can be used to solve 10^–y = 0.50. Find the approximate solution.

Answer 1

@agent0smith

Answer 2

here is the graph

Answer 3

Take a screenshot... wtf is a ggb file??

Answer 4

So what is y? there's only a p axis.

Answer 5

p is the function

Answer 6

That doesn't help figure out what y is though...

Answer 7

since there is a y here \[\Large 10^{–y}= 0.50\]

Answer 8

that's what I don't understand... how to get it

Answer 9

It's not a problem with you not understanding. The problem is the question sucks. There's no p in the question, yet there's one on the graph. There's no mention of what y is. The other axis isn't even labeled, so I don't know what it is either.

Answer 10

the graph is from geogebra, ignore the p

Answer 11

It's just labeling the function. It's from geogebra

Answer 12

Then where's the original graph given in the question? Take a screenshot of it.

Answer 13

I had to create the graph

Answer 14

There wasn't a graph given.

Answer 15

Then what did you use to make a graph? The question doesn't indicate anything about it.

Answer 16

That was the second part of the question this was the first part.
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.

Create a graph of the pH function.

Answer 17

lol this is why it's good to post the whole question right at the beginning, not just a part of it :P

So if we use y instead of p, the function is:
\[\Large y = –\log t\]and you need to find \[\Large 10^{–y}= 0.50\]

Answer 18

Use log properties. If \[\Large y = \log_a b \Large \text{ ....then.... } a^y = b\]

Answer 19

So with \[\Large y = –\log t\]first multiply both sides by -1 to get \[\Large -y = \log_{10} t\]
then use the log property above to get \[\Large 10^{–y}= t\]

Answer 20

Ok, so how do I get to y from that?

Answer 21

Read it all carefully and you should follow (assuming you've learned about log properties)

Now compare this to the last line above. What do you think t is?\[\Large 10^{–y}= 0.50 \]

Answer 22

0.50

Answer 23

Good, now all you need to do is find what y is, when t is 0.50 (from your graph).

Answer 24

Would the x-axis be the t values?

Answer 25

Yes

Answer 26

OK, thank you so much for your help! :)

Answer 27

What'd you get for y? btw the reason we can do it that way is again using log properties

Answer 28

I got 0.3

Answer 29

Using the same log property as before:

if \[\Large 10^{–y}= 0.50\]then \[\Large y = - \log 0.50\]

Answer 30

Yeah, I'd say 0.3 :)