Formula of a growth which can be represented in linear curve as

Options

A. `L_1 = L_0 + rt `
B. `L_0= L_1 + rt `
C. `W_1 = W_0 e^(rt)`
D. `W_0 = W_1 e^(rt)`

Answer

To find the formula for growth that can be represented by a linear curve, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Growth Types**:
- There are two main types of growth: Arithmetic and Geometric.
- Arithmetic growth is characterized by a constant addition of growth over time, while geometric growth involves exponential increase.

2. **Identifying Linear Growth**:
- Linear growth corresponds to arithmetic growth, where the increase is uniform over time.
- In arithmetic growth, the growth can be represented as a straight line on a graph, indicating that the growth rate remains constant.

3. **Defining the Variables**:
- Let:
- \( L_0 \) = Initial length of the organ at time \( t = 0 \)
- \( R \) = Rate of growth (how much the length increases per unit of time)
- \( T \) = Time elapsed

4. **Formulating the Equation**:
- The length of the organ at time \( t \) can be expressed as:
\[ L_1 = L_0 + R \times T \]
- Here, \( L_1 \) is the length of the organ at time \( t \).

5. **Understanding the Equation**:
- This equation shows that the final length \( L_1 \) is equal to the initial length \( L_0 \) plus the product of the growth rate \( R \) and the time \( T \).
- This linear relationship indicates that as time increases, the length increases at a constant rate, resulting in a linear curve when graphed.

6. **Conclusion**:
- Therefore, the formula of growth that can be represented by a linear curve is:
\[ L_1 = L_0 + R \times T \]