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Math Help - logarithm regression equation

  1. #1
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    Post logarithm regression equation

    The table shows Taiwan's nuclear power generation data in billions of killowatt hours. Let x=5 represent 1980, x=10 rep. 1985 and so on.

    Year Energy produced
    1980 7.8
    1985 27.8
    1990 31.6
    1995 33.9


    1) find natural logarithm regression equation for the data.
    y=-20.52 + 19.05 ln(x)

    I got this in my calculator..is it correct? Thanks!

    2) Predict when the nuclear power generation will reach 40 billion kilowatt hours.
    I have a question -- do you plug 40 billion into the x or the y? I think y, because it is total power, but just checking my work.

    When I plug 40 billion in for y, I come up with 21.47, which would be year 1996.
    Am I correct?
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    The table shows Taiwan's nuclear power generation data in billions of killowatt hours. Let x=5 represent 1980, x=10 rep. 1985 and so on.

    Year Energy produced
    1980 7.8
    1985 27.8
    1990 31.6
    1995 33.9


    1) find natural logarithm regression equation for the data.
    y=-20.52 + 19.05 ln(x)

    ok

    2) Predict when the nuclear power generation will reach 40 billion kilowatt hours.
    I have a question -- do you plug 40 billion into the x or the y? I think y, because it is total power, but just checking my work.

    When I plug 40 billion in for y, I come up with 21.47, which would be year 1996.
    Am I correct?

    y = 40 ... x = 23.97 ... about 1999
    ...
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  3. #3
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    would you plug in 40,000,000,000 or 40? because it's already in billions of kilowatts?
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  4. #4
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    Quote Originally Posted by live_laugh_luv27 View Post
    would you plug in 40,000,000,000 or 40? because it's already in billions of kilowatts?
    The table shows Taiwan's nuclear power generation data in billions of killowatt hours.
    .
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  5. #5
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    Quote Originally Posted by skeeter View Post
    .
    ok, when I plug in 40, I'm stuck at 60.52 = 19.05ln(x).
    When I try to divide to get rid of the ln(x) I'm coming up with completely wrong answers..help? Thanks
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  6. #6
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    Quote Originally Posted by live_laugh_luv27 View Post
    ok, when I plug in 40, I'm stuck at 60.52 = 19.05ln(x).
    When I try to divide to get rid of the ln(x) I'm coming up with completely wrong answers..help? Thanks
    60.52 = 19.05 \ln(x)

    divide by 19.05 ...

    \frac{60.52}{19.05} = \ln(x)

    convert the log equation into an exponential equation ...

    e^{\frac{60.52}{19.05}} = x

    pop this value into your calculator ...

    x = 23.97...
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    ok, thanks...so the end of 1998. or should I round it to 1999?
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  8. #8
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    Quote Originally Posted by live_laugh_luv27 View Post
    ok, thanks...so the end of 1998. or should I round it to 1999?
    I'm not going to hold your hand on this ... you decide.
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