The Arabidopsis plant is a Brilliant user

Classical Mechanics Level 2

The Arabidopsis plant, like most plants, generates sugars and starches during the day via photosynthesis. The sugars are metabolized, but the starches are stored for nighttime use so the plant can continue to grow and survive overnight. Unlike most plants, the Arabidopsis plant does something amazing. It uses starch at an (almost) constant rate $R$ each night and it chooses $R$ such that by the time morning comes, 95% of the stored starch is gone, independent of the length of the night! In other words, the plant knows when morning will come and does math to figure out how to last through the night.

Can you do the same math Arabidopsis does? On a standard 12 hour night, an Arabidopsis plant uses starch at a constant rate $R_1$ . You place an Arabidopsis plant in a dark room 2 hours early and the plant begins to use starch at a rate $R_2$ . What is $R_2/R_1$ ?

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Details and assumptions

At the beginning of both nights the plant has the same amount of starch.
At the ending of both nights the plant is exposed to sunlight at the same time in the morning.

The answer is 0.857.

5 solutions

Soaham Ganguly
Jan 13, 2014

Let us say that the starch consumed on the 12-hr night is S.

Thus the rate, R1 = S/12.

Now, the same amount of starch S will be consumed the next night as well, but due to the 2-hr delay, it will take 14 hrs.

Thus, R2= S/14

Dividing, we get R2/R1= 0.857

Nahom Yemane
Jan 3, 2014

12/14

Jabale Rahmat
Mar 14, 2014

Let assume plant had 1kg of stored starch. It uses 95 % of it at a rate of R1=0.95/12. In the second day the plant uses its starch at a rate of R2=0.95/14 R2/R1 = (19/280)/(19/240) = 0.857

Avisek Agarwal
Mar 6, 2014

Lets say the total starch be 12

So 12 starch / 12 hours = 1 starch per hour -- for standard night of 12 hours (R1)

But when 2 hours added to 12 hours it becomes 14 hours

And 12 starch / 14 hours = 0.86 (R2)

And 0.86/1= 0.86

Crazy Circle
Dec 18, 2013

Let the amount of starch in each case be x ( we ignore units for simplicity)

Therefore, in the whole nighttime, the plant uses 95/100 * x starch (its same in both cases) = K say.

Now, in the first case, the time period is 12 hours and so the rate is K / 12 and that of the 2nd case = K / 14

Therefore R 2 / R 1 = 12 / 14 = 6/7 = 0.857

The Arabidopsis plant is a Brilliant user

The answer is 0.857.

5 solutions

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