# differential application

• Apr 13th 2008, 02:40 PM
smschaefer
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)
• Apr 13th 2008, 02:47 PM
Kalter Tod
Quote:

Originally Posted by smschaefer
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.
• Apr 13th 2008, 02:51 PM
smschaefer
what is L'Hospital's rule?
• Apr 13th 2008, 04:25 PM
Mathstud28
It is
Quote:

Originally Posted by smschaefer
what is L'Hospital's rule?

The rule that states that if $\displaystyle \lim_{x \to c}\frac{f(x)}{g(x)}$ yields $\displaystyle \frac{\infty}{\infty}$ or $\displaystyle \frac{0}{0}$ there are more cases but those are the basic ones...then you can say that $\displaystyle \lim_{x \to c}\frac{f(x)}{g(x)}=\lim_{x \to c}\frac{f'(x)}{g'(x)}$
• Apr 13th 2008, 06:03 PM
TheEmptySet
Quote:

Originally Posted by smschaefer
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

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

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

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

as I goes to infinity we get

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

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

Good luck.