If `N =` population density at time t, then population density at time `t + 1` can be written as. `N_(t+1) = N_(t) + [(A+B)-(C+D)]`. Select the correct option for `A,B,C` and `D` in the above equation.

Options

A. `A` can be mortality and `B` can be natality
B. `B` can be immigration and `C` can be natality
C. `C` can be mortality and `D` can be immigration
D. `A` can be natality and `D` can be emigration.

Explanation

To solve the equation for population density at time `t + 1`, we need to understand the components represented by `A`, `B`, `C`, and `D` in the equation:

\[ N_{t+1} = N_t + [(A + B) - (C + D)] \]

### Step-by-Step Solution:

1. **Identify the Components of Population Change**:
- The population density at time `t` is represented as `N_t`.
- The change in population density from time `t` to `t + 1` can be influenced by several factors.

2. **Factors Contributing to Population Increase**:
- **Natality (A)**: This represents the birth rate, contributing positively to the population density.
- **Immigration (B)**: This represents individuals moving into the population from other areas, also contributing positively.

3. **Factors Contributing to Population Decrease**:
- **Mortality (C)**: This represents the death rate, which decreases the population density.
- **Emigration (D)**: This represents individuals leaving the population to join another, which also decreases the population density.

4. **Construct the Equation**:
- The equation can be summarized as:
\[ N_{t+1} = N_t + [(Natality + Immigration) - (Mortality + Emigration)] \]
- Thus, we can assign:
- \( A = \text{Natality} \)
- \( B = \text{Immigration} \)
- \( C = \text{Mortality} \)
- \( D = \text{Emigration} \)

5. **Final Formulation**:
- Therefore, the equation can be rewritten as:
\[ N_{t+1} = N_t + [(Natality + Immigration) - (Mortality + Emigration)] \]

### Conclusion:
The correct assignments for `A`, `B`, `C`, and `D` are:
- \( A = \text{Natality} \)
- \( B = \text{Immigration} \)
- \( C = \text{Mortality} \)
- \( D = \text{Emigration} \)