In exponential growth formula, `W_(t)=W_(0)e^(rt),e` denotes

Options

A. Final size
B. Time of growth
C. Base of natural logarithm
D. Growth rate.

Answer

To solve the question regarding the exponential growth formula \( W_t = W_0 e^{rt} \), we need to identify what the symbol \( e \) represents in this context.

### Step-by-Step Solution:

1. **Understand the Exponential Growth Formula**: The formula \( W_t = W_0 e^{rt} \) describes how a population (or size) grows over time. Here, \( W_t \) is the size at time \( t \), \( W_0 \) is the initial size, \( r \) is the growth rate, and \( t \) is the time.

2. **Identify the Components of the Formula**:
- \( W_t \): Final size at time \( t \)
- \( W_0 \): Initial size or population
- \( r \): Growth rate
- \( t \): Time of growth
- \( e \): A mathematical constant

3. **Determine the Meaning of \( e \)**: The symbol \( e \) is known as Euler's number, which is approximately equal to 2.71828. It is a fundamental constant in mathematics, particularly in calculus and exponential growth models.

4. **Conclude the Answer**: Since the question specifically asks what \( e \) denotes in the exponential growth formula, we conclude that \( e \) represents the base of the natural logarithm.

5. **Select the Correct Option**: Among the given options:
- Option 1: Final size
- Option 2: Time of growth
- Option 3: Base of natural logarithm
- Option 4: Growth rate

The correct answer is **Option 3: Base of natural logarithm**.

### Final Answer:
The \( e \) in the exponential growth formula \( W_t = W_0 e^{rt} \) denotes the **base of natural logarithm**.

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