Question

In plants, growth rate is expressed in Arithmetic and Geometric growth equations. Which equation is correct?

• A. \(L_0 = W_1 e^{rt}\)
• B. \(W_1 = W_0 e^{rt}\)
• C. \(W_0 = W_1 e^{rt}\)
• D. \(W_0 = L_0 + e^{rt}\)

Hint:

Geometric growth is commonly observed in populations with unlimited resources, where each individual reproduces at a constant rate.

Answer 1

The Correct Option is B

In the study of plant growth, two common types of growth models are used to describe how plants grow over time: arithmetic growth and geometric (exponential) growth. 
Arithmetic Growth:
In arithmetic growth, the growth rate remains constant, and the increase in size is by a fixed amount over equal time periods. The general equation for arithmetic growth is:

\[ W_1 = W_0 + (rt) \]

where:
\( W_1 \) is the weight or size of the plant at time \( t \),
\( W_0 \) is the initial weight or size of the plant,
\( r \) is the constant rate of growth,
\( t \) is the time.
Geometric Growth:
In geometric or exponential growth, the growth rate is proportional to the current size of the plant, leading to rapid increases as time progresses. The general equation for geometric growth is:

\[ W_1 = W_0 e^{rt} \]

where:
\( W_1 \) is the weight or size of the plant at time \( t \),
\( W_0 \) is the initial weight or size of the plant,
\( r \) is the rate of growth,
\( t \) is the time,
\( e \) is the base of the natural logarithm (approximately 2.718).
In this equation, the growth is not linear but increases exponentially. As the plant grows, its growth rate increases due to the larger size, resulting in more rapid growth.
Explanation of the Answer:
Among the options provided, the equation that best represents the geometric growth of a plant is:
 

\[ W_1 = W_0 e^{rt} \]

This equation matches the second option. The other options either suggest relationships that are incorrect in the context of geometric growth or describe arithmetic growth instead.
Thus, the correct equation for plant growth in the context of geometric growth is Option (2).