Question

ANYONE GOOD WITH LOGARTHIMS??!! PLZZ HELP

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 a pH above 7 is basic, or alkaline. Seawater has a pH just over 8, while lemonade has a pH of approximately 3.

Answer 1

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

2. 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.

3. The pool company has developed new chemicals that transform the pH scale. Using the pH function p(t) = –log10 t as the parent function, explain which transformation would result in a y-intercept. Use complete sentences and show all translations on your graph.

• p(t) + 1
• p(t + 1)
• –1 • p(t)

Answer 2

i hope this helps http://www.mathportal.org/calculators.php

Answer 3

Thanks. but this involves writing and explaining. and i would someone to explain it to me so I can solve it right.

Answer 4

that seems to be the only website the user knows, and th eonly posting they seem to be able to respond with. its as if they are trying to advertise the site.

Answer 5

yeah i noticed that as well

Answer 6

so you want to create a graph of this function:

p(t) = –log10 t .... the notation is a bit confusing. is it:\[log(10t)\]\[log_{10}(t)\]
or some other thing

Answer 7

yas! i got the graph using geogebra

Answer 8

so part 1 is taken care of :)

Answer 9

yay! now the 2nd question confuses me

Answer 10

how am i supposed to find it? do just input the function?

Answer 11

you are right in that it doesnt make a lot of sense, but replacing y with p(t) does seem reasonable.

Answer 12

oh wait i typed it wrong

Answer 13

it's not 10–y = 0.50. it's 10^-y = 0.50

Answer 14

that makes it better. log both sides of that

Answer 15

so log -y = log 0.50? i removed the ten since it's the common log

Answer 16

10^-y = 0.50

log(10^-y) = log(0.50)

-y log(10) = log(0.50)

-y = log(0.50)

y = -log(0.50)

so it looks like you what the point on your graph that has a t value of .50

Answer 17

i count 8 little hash marks, and 5 of them are under the graph ... so depending on how much of a perfectionist you are .. 5/8 seems to be a fair approximation. but im at a loss as to what that actually tells us at the moment

Answer 18

wait so when it says "Using complete sentences, explain how your graph can be used to solve 10–y = 0.50." how am i supposed to explain that?

Answer 19

10^-y = 0.50

Answer 20

you explain the steps you take to do what we just did ...

Answer 21

log both sides, and work the properties of logs; then use your graph to get an approximation

Answer 22

your class materials might have a more rigid wording for it, but those are the basics of it

Answer 23

yeah of course. how about the 3rd part?

Answer 24

i typed it wrong again -_- it's p(t) = –log_10 t , so the 10 is the base of the log dunction and t is the argument

Answer 25

so to clean it up, p(t) = -log(t) assuming the convention that log refers to base10

Answer 26

at the moment, the parent function has no y intercept. do you agree?

Answer 27

yeah. it's just getting closer and closer to the y axis but never touches it

Answer 28

so, if we take all the y values and scale them; all we do is stretch the graph up and down .... so it never moves closer to the y axis

if we take and add a constant to each y value, all we have done is shifted the graph up or down, and it never moves closer to the y axis.

what would you suggest is a good measure to move this thing to the left?

Answer 29

i thing it's p(t) + 1 , so it'd be p(t) = -log(t)+1 and we shift the graph to the left since it's supposed to be the opposite of the sign

Answer 30

does p(0) have a solution now? -log(0) + 1 = [??]

Answer 31

log(0) is still undefined and therefore this doesnt touch the x y axis, it only adds 1 to any p(t) value that was already present

Answer 32

if we modify the parent function: p(t) to change t to t+1 we get: p(t+1) = -log(t+1)

now, when t=0 we get: -log(0+1), does this give us a definable value?

Answer 33

no, but what does that have to do with the former one

Answer 34

sigh ....

we have a parent function, something that gets modified: p(t) = -log(t)

this parent function has no y intercept, there is no point (0,-log(0)) since log(0) has no definable value to it.

we want to modify the function so that when t=0, the function has some value tha tcan be attributed to it:

-p(t) = log(t) is no good, since log(0) is not definable

p(t)+1 = log(t)+1 is no good, since log(0) is not definable
undefined+1 is still undefined

p(t+1) = -log(t+1), for t=0 this gets us -log(1)
which should have a value that we can define for it

Answer 35

i get the parent function now, so we modify it by inserting one of the transformation to get y intercept.

Answer 36

we modify it by a left shift to get it to intercept the y axis, yes

Answer 37

p(t+1) shifts all the values of p(t) to the left, and allows us to cross over (intercept) the y axis

Answer 38

True, so that's the one that gives us the y intercept!

Answer 39

yep

Answer 40

great thank you so much:) i was totally stuck on this assignment but now i got it

Answer 41

good luck :)