Question

Anyone mind helping me understand a 3 part word problem for Algebra 2? Will post 1st part in comments

Answer 1

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.

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.

I need help understanding how to graph these first of all, I have desmos open, but I don't understand how to correctly graph this

Answer 2

is the p(t) function this?
\[\Large p(t) = -\log(10^t)\]
or is it this
\[\Large p(t) = -\log(10t)\]

Answer 3

1st one (:

Answer 4

wait, or is it this?
\[\Large p(t) = -\log_{10}(t)\]

Answer 5

if possible, post a screenshot of the problem so I can see the formula

Answer 6

hopefully this works

Answer 7

ok so it's \[\Large p(t) = -\log_{10}(t)\]

Answer 8

yep!

Answer 9

logs in desmos by default are in base 10

so \[\Large -\log_{10}(t) = -\log(t)\]

Answer 10

to graph, you simply type in `y = -log(x)`
use x in place of t

Answer 11

Ahh okay, I see that. Then would I put in the ph of 0 and 1 in for x or is that for something completely different?

Answer 12

p(t) is the pH
since y = p(t), y is the pH

if you wanted a pH of 0, you look where y is 0
this is all along the x axis

Answer 13

you can click on the root to have the coordinates pop up

Answer 14

for ph = 1, graph `y = 1` to go along with `y = -log(x)`. You may have to zoom in to see where they cross. You can click the intersection point to have the coordinates pop up

Answer 15

Ah got it! So they cross at 0.1,1, and that's all I had to do for the graph?

Answer 16

yes at (0.1, 1) so that means x = 0.1 and y = 1

x = 0.1 ---> t = 0.1 is the concentration of hydronium ions
y = 1 ---> p(t) = pH = 1 is the pH level which is very acidic. The ideal level is pH = 7

Answer 17

Okay awesome, I wrote that in for the first answer. Thank you!
I just need help with part 2, I can do part 3 by myself. What am I suppose to do here:


The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 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.

Just make an x and y chart I'm assuming?

Answer 18

`Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50`
so now x = 0.50

type in `x = 0.50` to have a vertical line graphed. This vertical line will cut through 0.5 on the x axis. Click the point of intersection between the vertical line and the curve. What coordinates pop up?

Answer 19

(0.5,0.301)

Answer 20

correct

Answer 21

so the pH level would be 0.301?

Answer 22

yes if the concentration of hydronium ions is 0.5

Answer 23

I'm not sure I understand the chemistry portion of this. Why would the pool maintenance man want the pH to be 0.301? That's very acidic. Wouldn't he want the pH to be closer to 7?

Answer 24

I would assume so yes, hang on a second let me see if there's any extra info.

Answer 25

yeah there's nothing else. I guess they just like having super acidic pools :p.
Okay, so last question is how do I change this into exponential function. it said to use y for the pH.

Answer 26

You would use the rule
if
\[\Large y = \log_{b}(x)\]
then
\[\Large x = b^y\]

Answer 27

`I guess they just like having super acidic pools`
yeah I don't know. This problem is very strange.

Answer 28

Ah okay, thank you for that equation, totally forgot what it was, I'm gonna go solve for that now. Thank you so much for your help! Appreciate it (: will medal and fan

Answer 29

you're welcome