S8. 3.7.10 at which photosynthesis takes place (min/max)

In summary, the rate of photosynthesis for a species of phytoplankton is modeled by the function $P=\dfrac{100I}{I^2 + I + 4}$ where I is the light intensity (measured in thousands of foot-candles). To find the light intensity at which P is a maximum, we derive the function $P'$ and set it equal to 0. This results in $I=\pm 2$, but it is unclear if $I=-2$ is a valid solution since intensity cannot be negative.
  • #1
karush
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10. The rate (in mg carbon$/m^3/h$) at which photosynthesis takes place for a species of phytoplankton is modeled by the function

$P=\dfrac{100I}{I^2 + I + 4} $
where I is the light intensity (measured in thousands of foot-candles). For what light intensity is $P$ a maximum?

OK I presume first we derive P'

$P'=\dfrac{ -100 (I^2 - 4)}{(I^2 + I + 4)}^2$

$P'(I)=0 $ at $x=\pm 2$

so far !
 
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  • #2
$P’=\dfrac{100(4-I^2)}{(I^2+I+4)^2}$

does $I =-2$ make sense given what $I$ represents?

So, how do you determine if $I=2$ determines a maximum?
 
  • #3
Can Intensity be negative?

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Can Intensity be negative?

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Can Intensity be negative?
 

Related to S8. 3.7.10 at which photosynthesis takes place (min/max)

1. What is S8. 3.7.10?

S8. 3.7.10 refers to the specific stage of photosynthesis in which the process takes place.

2. What is the minimum amount of photosynthesis that can occur at S8. 3.7.10?

The minimum amount of photosynthesis that can occur at S8. 3.7.10 is dependent on various factors such as the amount of light, water, and carbon dioxide available to the plant.

3. What is the maximum amount of photosynthesis that can occur at S8. 3.7.10?

The maximum amount of photosynthesis that can occur at S8. 3.7.10 is also dependent on the same factors as the minimum amount. However, the maximum amount may also be limited by the plant's genetic potential and environmental conditions.

4. How does S8. 3.7.10 differ from other stages of photosynthesis?

S8. 3.7.10 is the stage in which the light-dependent reactions of photosynthesis occur. This is when light energy is converted into chemical energy in the form of ATP and NADPH. Other stages of photosynthesis, such as the Calvin cycle, involve the use of these energy molecules to produce glucose.

5. Can photosynthesis occur at S8. 3.7.10 without the presence of light?

No, photosynthesis at S8. 3.7.10 cannot occur without the presence of light. This stage specifically requires light energy to drive the reactions that produce ATP and NADPH. Without light, the process of photosynthesis cannot continue.

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