Exponential growth is expressed as

Options

A. `Lt = L_(0)+rt`
B. `L_(0) = Le^(rt)`
C. `W_(1)=W_(0)+e^(rt)`
D. `W_(0)=W_(1)e^(rt)`

Answer

To express exponential growth mathematically, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Exponential Growth**:
Exponential growth refers to the increase in a quantity where the growth rate is proportional to the current amount. This is often seen in populations, such as bacteria.

2. **Identifying the Formula**:
The general formula for exponential growth can be expressed as:
\[ W_t = W_0 e^{rt} \]
where:
- \( W_t \) is the final amount after time \( t \),
- \( W_0 \) is the initial amount,
- \( r \) is the growth rate,
- \( t \) is the time,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

3. **Interpreting the Variables**:
- \( W_0 \) represents the initial quantity (e.g., the initial number of bacteria).
- \( W_t \) represents the quantity after time \( t \).
- \( r \) indicates how fast the growth occurs.
- \( t \) is the duration over which the growth is measured.

4. **Final Expression**:
From the above understanding, we can conclude that the expression for exponential growth is:
\[ W_1 = W_0 e^{rt} \]
This matches option D from the question.

### Conclusion:
The correct expression for exponential growth is \( W_1 = W_0 e^{rt} \).

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