The question asks for the specific rate at which new individuals are added to a population, considering the population's size.
The rate of increase in population size due to births over a time interval $\Delta t$ is $\frac{\Delta N_n}{\Delta t}$. This represents the number of births per unit of time.
To find the natality rate per unit of population, we need to normalize this rate by the initial population size ($N$). This tells us the average number of births per individual in the population during the time interval.
The formula becomes:
Natality Rate Per Unit Population = $\frac{\text{Number of Births}}{\text{Initial Population Size} \times \text{Time Interval}}$
Substituting the given variables:
Natality Rate Per Unit Population = $\frac{\Delta N_n}{N \times \Delta t}$
This matches the expression $\frac{\Delta N_n}{N\Delta t}$.