Exponential Growth Model

What is the exponential growth model?

A population growth model where individuals reproduce at any time, leading to continuous growth and a J-shaped curve. Mathematically, it follows:

• dN/dt = rN

What does the symbol N represent in the exponential growth equation?

N represents the population size

What does the symbol r represent in the equation dN/dt = rN?

The growth rate per individual (intrinsic growth rate).

Write the instantaneous growth rate equation and explain its meaning.

The instantaneous growth rate is: dN/dt = rN

• And it tells us how much the population size is changing at any particular instant in time.

What is the shape of the graph for exponential growth?

A J-shaped curve, similar to geometric growth but slightly steeper due to continuous increase.

How does exponential growth differ from geometric growth in terms of time?

Exponential growth is continuous (reproduction can occur at any time), whereas geometric growth occurs in fixed time intervals.

What is biotic potential?

The maximum possible growth rate of a population under ideal conditions with unlimited resources.

How is biotic potential related to r ?

Under ideal conditions, the intrinsic growth rate r reaches its maximum value, representing the biotic potential.

What is the relationship between dN/dt and N in the exponential model? 

dN/dt is proportional to N ; as N increases, the rate of change ( dN/dt ) also increases linearly with N. 

If r = 0.2 per time unit and N = 100, what is dN/dt?

dN/dt = rN

= 0.2 × 100

= 20 individuals per time unit