select the correct representation of den...

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

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

`N_(t+1) = N_t[(B+I)+(D+E)]`

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

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

Text Solution

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The correct Answer is:

To solve the question regarding the correct representation of the density of population (N) after a period of time \( t + 1 \), we need to consider the factors that affect population change over time. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Variables 1. **N**: Represents the density of the population at time \( t \). 2. **b**: Represents the number of births in the population. 3. **d**: Represents the number of deaths in the population. 4. **i**: Represents immigration, or the number of individuals coming into the population. 5. **e**: Represents emigration, or the number of individuals leaving the population. ### Step 2: Establish the Initial Population At time \( t \), the population density is represented as \( N_t \). ### Step 3: Determine Changes in Population To find the population density at time \( t + 1 \) (denoted as \( N_{t+1} \)), we need to account for the changes in population due to births, deaths, immigration, and emigration. ### Step 4: Formulate the Equation The change in population can be expressed as: \[ N_{t+1} = N_t + b + i - d - e \] Where: - \( N_t \) is the population density at time \( t \). - \( b \) is added to account for births. - \( i \) is added to account for immigration. - \( d \) is subtracted to account for deaths. - \( e \) is subtracted to account for emigration. ### Step 5: Rearranging the Equation We can rearrange the equation to clearly show the relationship: \[ N_{t+1} = N_t + (b + i - d - e) \] ### Step 6: Identify the Correct Representation From the rearranged equation, we can see that the correct representation of the density of population after a period of time \( t + 1 \) is: \[ N_{t+1} = N_t + b + i - d - e \] This matches with the first option provided in the question. ### Conclusion Thus, the correct representation of the density of population \( N \) after a period of time \( t + 1 \) is: \[ N_{t+1} = N_t + b + i - d - e \] ---

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