Arithmetic growth curve is represented by which of the following equation?

Options

A. (a) `w_(t) = w_(0)e^(rt)`
B. (b) `L_(0) = L_(t) + rt`
C. (c) `L_(t) = L_(0) + rt`
D. (d) `2L_(t) = L_(0) - rt`

Answer

To determine the equation that represents an arithmetic growth curve, we can follow these steps:

### Step 1: Understand the Concept of Arithmetic Growth
Arithmetic growth occurs when a quantity increases by a constant amount over equal intervals of time. This means that the growth can be described using arithmetic progression.

### Step 2: Identify the Characteristics of the Growth Curve
In an arithmetic growth curve, the growth is linear, which means that if you plot the growth against time, you will get a straight line. The growth at any time \( t \) can be expressed as the initial amount plus a constant rate multiplied by time.

### Step 3: Analyze the Given Options
We need to evaluate the provided equations to find which one represents arithmetic growth:

1. **Option A**: \( wt = w_0 e^{rt} \) - This represents exponential growth, not arithmetic growth.
2. **Option B**: \( L_0 = L_T + RT \) - This equation does not correctly represent growth and is not suitable.
3. **Option C**: \( L_T = L_0 + RT \) - This equation indicates that the growth at time \( T \) is equal to the initial amount plus the product of the rate of growth and time, which is characteristic of arithmetic growth.
4. **Option D**: This option describes a doubling amount, which is not relevant to arithmetic growth.

### Step 4: Select the Correct Equation
From the analysis, we find that **Option C** \( L_T = L_0 + RT \) is the correct representation of an arithmetic growth curve.

### Conclusion
The equation that represents the arithmetic growth curve is:
\[ L_T = L_0 + RT \]