select the correct representation of density of population (N) which can be expressed after a period of time `t+1`.

Options

A. `N_(t+1) = N_t+[(B+I) - (D+E)]`
B. `N_(t+1) = N_t[(B+I)+(D+E)]`
C. `N_t = N_(t+1) + [(B+I)-(D+E)]`
D. `N_(t+1) = N_t[(B+I) + (D-E)]`

Answer

To solve the question regarding the correct representation of the density of population (N) after a period of time \( t + 1 \), we can follow these steps:

### Step 1: Understand the Components
We need to identify the components that affect population density:
- **Natality (b)**: The birth rate, which increases the population.
- **Immigration (I)**: The arrival of new individuals into the population, which also increases the population.
- **Mortality (D)**: The death rate, which decreases the population.
- **Emigration (E)**: The departure of individuals from the population, which decreases the population.

### Step 2: Set Up the Equation
The change in population density over time can be expressed as:
\[ N_{t+1} = N_t + \text{(increase in population)} - \text{(decrease in population)} \]
Where:
- \( N_t \) is the population density at time \( t \).
- The increase in population is due to natality and immigration.
- The decrease in population is due to mortality and emigration.

### Step 3: Write the Formula
From the components identified, we can write the formula for population density at time \( t + 1 \):
\[ N_{t+1} = N_t + b + I - D - E \]
Where:
- \( b \) is natality,
- \( I \) is immigration,
- \( D \) is mortality,
- \( E \) is emigration.

### Step 4: Simplify the Equation
Combining the terms, we can express the equation as:
\[ N_{t+1} = N_t \cdot b + I - D + E \]
This reflects the changes in population density after the time period \( t + 1 \).

### Final Representation
Thus, the correct representation of the density of population \( N \) after a period of time \( t + 1 \) is:
\[ N_{t+1} = N_t \cdot b + I - D + E \]