If b=65 and d is =45 ,N=100 than find out dN/dt

Options

A. 2000
B. 1000
C. 200
D. 100

Answer

To solve the problem, we need to use the formula for the rate of change of the population size (dN/dt) in the context of exponential growth. The formula is given by:

\[ \frac{dN}{dt} = (b - d) \times N \]

Where:
- \( b \) is the birth rate,
- \( d \) is the death rate,
- \( N \) is the current population size.

### Step-by-Step Solution:

1. **Identify the values given in the problem:**
- Birth rate \( b = 65 \)
- Death rate \( d = 45 \)
- Population size \( N = 100 \)

2. **Substitute the values into the formula:**
\[ \frac{dN}{dt} = (b - d) \times N \]
\[ \frac{dN}{dt} = (65 - 45) \times 100 \]

3. **Calculate the difference between birth rate and death rate:**
\[ 65 - 45 = 20 \]

4. **Multiply the result by the population size:**
\[ \frac{dN}{dt} = 20 \times 100 \]
\[ \frac{dN}{dt} = 2000 \]

5. **Conclusion:**
The rate of change of the population size \( \frac{dN}{dt} \) is 2000.

### Final Answer:
\[ \frac{dN}{dt} = 2000 \]

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