Question

The formula for exponential population growth is -

• A. dN/dt = rN
• B. dt/dN = rN
• C. dN/rN = dt
• D. rN/dN = dt

Answer 1

The Correct Option is A

 The exponential population growth model is a fundamental concept in biology that describes how populations can grow under ideal conditions with unlimited resources. The formula for exponential population growth can be expressed as:

\(\frac{dN}{dt} = rN\)

Where:

• \(N\) is the population size.
• \(t\) is time.
• \(r\) is the intrinsic rate of increase (often called the growth rate).

This formula means that the change in population size (dN) over the change in time (dt) depends on the current population size (N) and the growth rate (r).

Let's analyze why

dN/dt = rN

is the correct option:

 

1. The equation \(\frac{dN}{dt} = rN\) directly represents the exponential growth model, where the growth is proportional to the current size of the population.
2. Other options do not accurately capture this proportional relationship:
   • \(\frac{dt}{dN} = rN\): This implies the inverse relationship, which is incorrect for depicting exponential growth.
   • \(\frac{dN}{rN} = dt\): This rearrangement doesn't fit the biological context of continuous growth and isn't standard in describing exponential growth.
   • \(\frac{rN}{dN} = dt\): This wrongly represents the relationship and does not match the consistent increase described in exponential growth.

Hence, the relationship given by \(\frac{dN}{dt} = rN\) is the correct choice for representing exponential population growth.