How do botanists know the exact age of a tree?

In climates that regularly have a season of growth and a season of rest each year, trees grow with a series of ‘annual rings’, which can be seen in a cross section of the trunk. (See image below.) In some trees these rings are clearly marked and we have only to count them to have a good idea of the tree’s age. Sometimes, however, the count may not tell the entire story. So long as the tree goes on living healthily a fresh ring will be formed each year, but the growth of a tree may be interrupted and begin again during the same season, and then two false rings appear. The false rings are much thinner than the true rings and do not always extend right round the tree. A drought or a severe attack by caterpillars or other insects may lead to interrupted growth and give rise to the false rings. The tree forms both true and false rings by adding new wood around the trunk just beneath the bark.
Botanists can distinguish between one year’s growth and the next because the wood added in the earlier part of the year is different from the wood added later in the summer. In the spring, when growth begins and fresh leaves and twigs are put out, much water is needed in the crown of the tree to supply these new, springtime cells with thin walls and wide openings so that the water can rise rapidly. In summer, however, when there is less demand for water, the cells formed are thick walled and have small openings. That explains why the summer wood in each year’s growth is heavier and stronger than the spring wood. 

Additional reading:
Botany (Wikipedia)
Dendrochronology (Wikipedia)

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