The formula of growth rate for population in a given time is

Options

A. dt/dN= rN
B. dt/rN = dN
C. rn/dN=dt
D. dN/dt=rN

Answer

To determine the formula for the growth rate of a population over a given time, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Population Growth**:
- Population growth can be described in terms of birth rates and death rates. The growth rate indicates how the population size changes over time.

2. **Defining Variables**:
- Let \( N \) represent the population size.
- Let \( B \) represent the birth rate (per capita births).
- Let \( D \) represent the death rate.

3. **Growth Rate Formula**:
- The change in population size over time can be expressed as:
\[ \frac{dN}{dt} = B - D \]
- Here, \( \frac{dN}{dt} \) represents the rate of change of the population size.

4. **Expressing Growth Rate in Terms of Population**:
- The growth rate can also be expressed as a function of the current population size:
\[ \frac{dN}{dt} = rN \]
- In this equation, \( r \) is the intrinsic rate of natural increase, defined as \( r = B - D \).

5. **Final Formula**:
- Therefore, the formula for the growth rate of the population in a given time is:
\[ \frac{dN}{dt} = rN \]
- This indicates that the population grows exponentially when the growth rate \( r \) is positive.