# The Arabidopsis plant is a Brilliant user

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 $R_2/R_1$?

For more reading, check this out.

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.
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