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anonymous

  • one year ago

Pre-Cal :)))

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  1. anonymous
    • one year ago
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    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.

  2. phi
    • one year ago
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    does p(t) = −log10t. mean \[ p(t)= - \log_{10} t \] or \[ p(t) = −\log(10t)\]?

  3. anonymous
    • one year ago
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    The 1st one lol!

  4. phi
    • one year ago
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    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

  5. anonymous
    • one year ago
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    Ok, then how would u graph it?

  6. phi
    • one year ago
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    first, what is the log of 10^-3 ? \[ \log_{10} \left(10^{-3} \right) = \]

  7. anonymous
    • one year ago
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    0.001?

  8. phi
    • one year ago
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    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 ?

  9. anonymous
    • one year ago
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    -3

  10. phi
    • one year ago
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    ok. \[ p(t)= - \log_{10} t \\= -1 \cdot \log(0.001) \\= -1 \cdot -3 = 3 \]

  11. phi
    • one year ago
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    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)

  12. anonymous
    • one year ago
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    yes, I think I can. How could I graph this using technology?

  13. phi
    • one year ago
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    if you have geogebra , you type in the equation

  14. anonymous
    • one year ago
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    I dont have that/ know what that is lol :)

  15. anonymous
    • one year ago
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    I have desmos.com but I wouldnt know how to type that in

  16. anonymous
    • one year ago
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    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.

  17. phi
    • one year ago
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    just type in y= -log(x)

  18. anonymous
    • one year ago
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    oH! Hahaha thanks :)

  19. anonymous
    • one year ago
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    What about the 2nd part of the question?

  20. phi
    • one year ago
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    zoom in on your graph, and click on the curve when it has y=0.5 what do you get for the x value ?

  21. anonymous
    • one year ago
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    I got (0.316,0.5)

  22. phi
    • one year ago
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    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 \[ 10^{-y} = t \\ t= 10^{-y} \]

  23. phi
    • one year ago
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    yes, 0.316 is good using the exponential equation \[ t= 10^{-0.5} = \frac{1}{\sqrt{10}} = 0.316228\]

  24. anonymous
    • one year ago
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    So, we just converted it right? And that would be the answer to the question?

  25. phi
    • one year ago
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    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)

  26. anonymous
    • one year ago
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    Yes! Thanks so much<3

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