`(dN)/(dt) =rN`
How does the increase and decrease in the value of 'r' affect the population size.

Explanation

To understand how the increase and decrease in the value of 'r' affects the population size, we can analyze the equation given:

1. **Understanding the Equation**: The equation \( \frac{dN}{dt} = rN \) describes the rate of change of a population size (N) over time (t). Here, \( r \) represents the intrinsic rate of increase, which is the difference between the birth rate and the death rate of the population.

2. **Effect of Increasing 'r'**:
- When the value of 'r' increases, it indicates that the per capita rate of increase is higher. This means that either the birth rate has increased, the death rate has decreased, or both.
- As a result, the term \( rN \) becomes larger, leading to a greater rate of change in population size (\( \frac{dN}{dt} \)).
- Therefore, if 'r' increases, the population size (N) will also increase more rapidly over time.
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