Death rate signifies the number of deaths of an individual group of organism over a certain period of time. Reduction in death rate means that the number of organisms dying in a certain period of time reduces and since the number of deaths reduces, the population of penguins will increase. Also the increased population will lead to increased competition among the penguins as the resources remains constant.
So, a sudden drop in the death rate means that while everything stays the same, less penguins are dying: the penguins are living longer! This means that the population will increase: there will be more penguins at all times!
