The demographic transition, where population growth slows in developed countries, is due to a (n) :

Decline in fertility and mortality rate

Explanation:

Developed countries have higher tendency for low mortality rate and fertility. This is the later stage of demographic transition as opposed to the early stages of demographic transition which is seen in developing countries. The rationale behind the different demography in developed countries is mostly because there is better standard of living in these countries and so individuals are able to live longer lives.