Question

A population numbers 10,000 organisms initially and decreases by 1.8% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P=a*bᵀ where P

Answer 1

Exponential growth of bacteria is showcased by their population doubling every hour in ideal conditions, leading to a significant increase. A J-shaped growth curve is produced when plotted over time, reflecting the accelerating population growth rate until resources limit further expansion.

Step-by-step explanation:

The concept of exponential growth is well illustrated by the growth of bacterial populations. When bacteria, such as prokaryotes, have access to abundant resources, they can reproduce rapidly through a process called prokaryotic fission. This typically takes about an hour for many species. Starting with 1000 bacteria, the population will double in size every hour, assuming unlimited nutrients. The growth rate accelerates with each reproductive generation, leading to a substantial increase in population over a short period. For instance, after one day or 24 hours, the bacterial count could exceed 16 billion from the original 1000, showing a J-shaped growth curve when plotted over time.

Exponential growth is characterized by the rate of increase becoming greater as the population grows. This pattern continues until resources become limited, at which point the growth rate will slow and eventually level off, resulting in a logistic growth curve.