If b is represent `to` birth rate
If d is represent `to` death rate
if dN is represent `to` increase or decrease in population size
Then exponetial growth is represented by

Options

A. `dN//dt=(b+d)N`
B. `dN//dt=(b-d)N`
C. `dN//dt=(d-b)N`
D. `dN//dt=(d-b)^N`

Answer

To represent exponential growth in a population, we start with the definitions provided in the question:

1. **Identify Variables**:
- Let \( b \) = birth rate
- Let \( d \) = death rate
- Let \( N \) = population size
- Let \( dN \) = change in population size

2. **Understand the Change in Population Size**:
- The change in population size over time can be expressed as \( \frac{dN}{dt} \), which represents the rate of change of population size with respect to time.

3. **Formulate the Equation**:
- The change in population size can be calculated as the difference between the birth rate and the death rate multiplied by the population size:
\[ \frac{dN}{dt} = (b - d) \cdot N \]

4. **Introduce the Intrinsic Rate of Natural Increase**:
- We can denote \( r \) as the intrinsic rate of natural increase, where \( r = b - d \).
- Thus, the equation can be rewritten as:
\[ \frac{dN}{dt} = r \cdot N \]

5. **Final Representation of Exponential Growth**:
- Therefore, the equation representing exponential growth is:
\[ \frac{dN}{dt} = (b - d) \cdot N \]
or equivalently,
\[ \frac{dN}{dt} = r \cdot N \]

6. **Conclusion**:
- The correct representation of exponential growth in terms of the variables given is:
\[ \frac{dN}{dt} = (b - d) \cdot N \]