If N is the population density at time 't', its density at time t+1 w…

The correct answer is Option (1) → N_t+1 = N_t + [(B + I) - (D + E)]

The density of a population changes through four processes. Two of them add individuals and two remove them:

    Natality (B): the number of births — adds
    Immigration (I): individuals coming in from elsewhere — adds
    Mortality (D): the number of deaths — removes
    Emigration (E): individuals leaving for elsewhere — removes

So the density one unit of time later is the old density, plus what is added (B + I), minus what is removed (D + E).

(1) N_t+1 = N_t + [(B + I) - (D + E)] — Correct. Births and immigrants are added; deaths and emigrants are taken away.

(2) N_t+1 = N_t + [(B + E) - (D + I)] — Incorrect. It adds emigrants, who have left, and takes away immigrants, who have come in. E and I are swapped.

(3) N_t+1 = N_t + [(B - I) + (D - E)] — Incorrect. It takes away immigrants and adds deaths. Both are the wrong way round.

(4) N_t+1 = N_t + [(B - E) + (D - I)] — Incorrect. It adds deaths and takes away immigrants.

NCERT Extract:
Population Growth – “Emigration is the number of individuals of the population who left the habitat and gone elsewhere during the time period under consideration. So, if N is the population density at time t, then its density at time t +1 is Nt+1 = Nt + [(B + I) – (D + E)] You can see from the above equation (Fig. 11.2) that population density will increase if the number of births plus the number of immigrants (B + I) is more than the number of deaths plus the number of emigrants (D + E).”

Figure 11.2