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Math Help - differential application

  1. #1
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    differential application

    Biomathematics have proposed many different functions for describing the effects of light on the rate at which photosynthesis can take place. If the function is to be realistic, then it must exhibit the photo inhibition effect. That is the rate of production P of photosynthesis must decrease to 0 as the light intensity I reaches higher and higher levels. Which of the following formulas for P, with a and b constant, may be used?

    1) P= (aI)/(b+I) or 2) P= (aI)/(b+I^2)
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  2. #2
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    Quote Originally Posted by smschaefer View Post
    Biomathematics have proposed many different functions for describing the effects of light on the rate at which photosynthesis can take place. If the function is to be realistic, then it must exhibit the photo inhibition effect. That is the rate of production P of photosynthesis must decrease to 0 as the light intensity I reaches higher and higher levels. Which of the following formulas for P, with a and b constant, may be used?

    1) P= (aI)/(b+I) or 2) P= (aI)/(b+I^2)
    It would be the 2nd one because if you were to use L'Hopital's rule on the first formula, you would not have a function that approached zero at very large values of I. In the second one, you would have a constant over infinity, or zero.
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  3. #3
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    what is L'Hospital's rule?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    It is

    Quote Originally Posted by smschaefer View Post
    what is L'Hospital's rule?
    The rule that states that if \lim_{x \to c}\frac{f(x)}{g(x)} yields \frac{\infty}{\infty} or \frac{0}{0} there are more cases but those are the basic ones...then you can say that \lim_{x \to c}\frac{f(x)}{g(x)}=\lim_{x \to c}\frac{f'(x)}{g'(x)}
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  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by smschaefer View Post
    Biomathematics have proposed many different functions for describing the effects of light on the rate at which photosynthesis can take place. If the function is to be realistic, then it must exhibit the photo inhibition effect. That is the rate of production P of photosynthesis must decrease to 0 as the light intensity I reaches higher and higher levels. Which of the following formulas for P, with a and b constant, may be used?

    1) P= (aI)/(b+I) or 2) P= (aI)/(b+I^2)
    You don't need L'hospitals rule to solve this problem

    p=\frac{aI}{b+I}

    if we multiply the numerator and denominator by \frac{\frac{1}{I}}{\frac{1}{I}}

    p= \frac{\frac{1}{I}}{\frac{1}{I}}\frac{aI}{b+I}=\fra  c{a}{\frac{b}{I}+1}

    as I goes to infinity we get

    \frac{a}{\frac{b}{I}+1}=\frac{a}{0+1}=a

    try a similar trick with the 2nd one and you will see that it does go to zero.

    Good luck.
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