Question

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 1

@ganeshie8 @whpalmer4 @mathstudent55

Answer 2

Please help

Answer 3

@mathmale

Answer 4

Do you know the equation for pH?

Answer 5

If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects on 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.

Answer 6

Okay so in our question, concentration of ions is increased by 1/2. Can you form the equation for that from basic equation of pH?

Answer 7

would the base be 0.5?

Answer 8

Never! pH is always done with base 10. You only have to change the concentration part!

Answer 9

ok, sorry, im just a bit slow with this

Answer 10

It's okay. Take your time :)

Answer 11

p(h)=log(10)(0.5)

Answer 12

\[\log_{10} (0.5)\]

Answer 13

If the original equation is p(t) = −log10t.

Wouldn't it be p(t) = −log10(t+0.5) ??

Answer 14

that makes sense, like i said im a little slow with this so itll be a bit hard for me

Answer 15

Okay. Can you try it with that input?

Answer 16

i dont know what you mean.

Answer 17

Graph it?

Answer 18

I can do that.

Answer 19

Let's see that since the question asks you to.

Answer 20

That format doesnt work on my pc.

Answer 21

o, let me try another, sorry about that

Answer 22

does that work?

Answer 23

Good. Sorry got bsy.

Answer 24

no problem

Answer 25

Now you need to convert it into exponential function

For that write p(t) as y then take 10^y from the equation.

Answer 26

y=-log(t+0.5)?

Answer 27

yes take 10^y from that.

Answer 28

y-10^y=-log(t+0.5)?

Answer 29

Nope.

First -log A=log 1/A

Use that

Answer 30

what does the A stand for, (t+0.5)?

Answer 31

Yup

Answer 32

ok

Answer 33

\[-\log_{10} (t+0.5)=\log(1)/(t+0.5) \]

Answer 34

thats what i interpreted

Answer 35

This equals y

So 10^y=log(1/t+0.5))

This is the expression in exponential form.

Answer 36

ok, thank you so much. I really appreciate it.

Answer 37

yw :)

Answer 38

Wait u shoudn't write log in the final equation! Sorry abt that!

Answer 39

so 10^y=(1/(t+0.5))

Answer 40

Yep.

Answer 41

ok thx

Answer 42

im gonna close the question now

Answer 43

ok?

Answer 44

Sure! This indeed took some time isn't it? :)

Answer 45

yes