Simply stated, plants do not grow any slower at night than they do during the day. Plants do stop photosynthesizing at night, but the act of respiration, which is how plants create energy and grow, continues at night at more or less the same level as it does during the day, or even faster.
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Respiration and Photosynthesis
Photosynthesis is the process through which plants turn light into the energy they can synthesize and use. This process can only occur when light is present, which is during the day under natural growing circumstances. Respiration is the process in which plants take the sugar and oxygen created through photosynthesis and turn them into the carbohydrates essential to the plants' growth. Assuming photosynthesis has occurred during the day, respiration will occur at night at an equal rate as during the day, or even faster at night than during the day.
It is a common misconception that plants can only grow while photosynthesizing, as most people don't realize that respiration is actually a function in and of itself. Photosynthesis produces energy from the sun in the form of sugars and stores this energy. Respiration is the process through which plants combine these sugars with oxygen to form carbohydrates, with which the plant grows.
Chloroplasts are tiny organelles covering the leaf of a plant which give the plant its green color. They are responsible for capturing light energy and photosynthesizing it into the stored energy used for respiration. Chloroplasts shrink at night as they release stored energy and cease photosynthesis; buds and blooms close up at night since their function is reproduction, by and large supported by insects that are active in the day. Respiration and plant growth are not affected by either of these parts of the plant directly and thus are unaffected at night.
Through his research and observation, Darwin concluded that plants actually grew more at night than during the day. His theory was that plants would grow faster and more suddenly when they received less light in an attempt to get more light. For example, a seedling growing slower than those around it will be blocked from the sun by taller seedlings; in an attempt to reach more sunlight, it will bolt and grow taller. Darwin believed that this adaptation followed through to nighttime and that as a result all plants grew faster at night.
Building on Darwin
Biologists have recently found that plants actually possess a gene that regulates rhythmic growth. This research has essentially confirmed Darwin's theory, showing that plants tend to grow most rapidly just before dawn, usually in spurts that far surpass the rate of growth experienced by the plants at other times during the day. Much of this has to do with expending remaining energy stored the previous day before the next day comes to pass.