Find out dN/dt when carrying capacity is 400 , population size is 300 and r is =0.01.

Options

A. 0.01
B. 0.8
C. 0.75
D. 0.45

Answer

To find \( \frac{dN}{dt} \) using the given parameters, we can follow these steps:

### Step 1: Understand the formula
The formula to calculate the change in population size over time is given by:

\[ \frac{dN}{dt} = rN \left( \frac{K - N}{K} \right) \]

Where:
- \( N \) is the current population size
- \( K \) is the carrying capacity
- \( r \) is the intrinsic rate of natural increase

### Step 2: Identify the given values
From the question, we have:
- \( K = 400 \) (carrying capacity)
- \( N = 300 \) (current population size)
- \( r = 0.01 \) (intrinsic rate of natural increase)

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:

\[ \frac{dN}{dt} = 0.01 \times 300 \left( \frac{400 - 300}{400} \right) \]

### Step 4: Simplify the equation
Calculate \( K - N \):

\[ K - N = 400 - 300 = 100 \]

Now substitute this back into the equation:

\[ \frac{dN}{dt} = 0.01 \times 300 \left( \frac{100}{400} \right) \]

### Step 5: Simplify further
Calculate \( \frac{100}{400} \):

\[ \frac{100}{400} = 0.25 \]

Now substitute this value back into the equation:

\[ \frac{dN}{dt} = 0.01 \times 300 \times 0.25 \]

### Step 6: Calculate the final value
Now calculate \( 0.01 \times 300 \):

\[ 0.01 \times 300 = 3 \]

Now multiply this by \( 0.25 \):

\[ \frac{dN}{dt} = 3 \times 0.25 = 0.75 \]

### Final Answer
Thus, the value of \( \frac{dN}{dt} \) is:

\[ \frac{dN}{dt} = 0.75 \]

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