1. 'Fertility' refers to the ability to produce children. Here this is not the reason for a rise in the population of the place/country. Instead the speed (rate) at which people are dying is not as fast as it used to be ("a sharp decline"), so if people die when they are older (the death rate) the number of people currently alive is higher.
2. At any one moment, when no birth control is in use ie contraceptives, 4 percent of the population is producing children (not very high), and this fact is related to 1).
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