Question

Describe in brief the exponential growth curve with the help of a suitable example.

Hint:

Exponential growth is characteristic of populations that have unlimited resources and no environmental constraints.

Answer 1

Step 1: Define Exponential Growth. - Exponential growth occurs when the growth rate of a population is proportional to the current population size, leading to rapid increase over time. The population grows without any limitation (in ideal conditions).
Step 2: Characteristics of Exponential Growth. - Exponential growth is depicted as a J-shaped curve. It starts slow, but as the population increases, the growth accelerates exponentially. - Formula: \[ N(t) = N_0 e^{rt} \] where \( N(t) \) is the population size at time \( t \), \( N_0 \) is the initial population size, \( r \) is the rate of growth, and \( t \) is the time.
Step 3: Example of Exponential Growth. - Bacteria in a culture: In a controlled environment with unlimited resources, bacteria reproduce rapidly through binary fission, causing the population to grow exponentially.
Final Answer: Exponential growth occurs when a population grows at a constant rate, leading to rapid increases over time, as seen in bacterial cultures under ideal conditions.