Final answer:
Using the logistic growth equation, approximately 83 new individuals will be added to the population in one year, resulting in a new population size of 583 individuals.
Step-by-step explanation:
The question concerns the concept of logistic growth in a population of organisms, and how to calculate the expected growth over time given the growth rate (r) and the carrying capacity (K). The carrying capacity is the maximum population size an environment can sustain given the available resources. In this scenario with a population of 500 individuals, a carrying capacity of 3000, and a growth rate of 0.2, we expect to see growth that adheres to the logistic model.
The logistic growth equation can be represented as:
Population growth = rN(K-N)/K
Where:
- r is the growth rate
- N is the current population size
- K is the carrying capacity of the environment
- K-N indicates the remaining population capacity
To calculate the number of new individuals added in one year, we plug the values into the logistic growth equation:
Population growth = 0.2 × 500 × (3000 - 500) / 3000
Population growth = 0.2 × 500 × 2500 / 3000
Population growth = 100 × 2500 / 3000
Population growth = 250,000 / 3000
Population growth = approximately 83 new individuals
So at the end of one year, the population will increase by approximately 83 individuals. Thus, the new population size after one year would be:
New population size = Initial population + Population growth
New population size = 500 + 83
New population size = 583 individuals
Since the student hasn't specified other time frames, we have calculated the growth for one year only. Note that as the population grows closer to the carrying capacity, the number of new individuals added each year according to the logistic model will decrease.