Exponential and logistic growth in populations - Khan Academy Exponential growth has time in the exponent, causing a rapid increase in population size In real-world situations, logistic growth is more accurate due to environmental constraints Logistic growth models population growth with a natural carrying capacity, creating an S-shaped curve
Logistic growth versus exponential growth - Khan Academy Exponential growth presumes infinite resources, resulting in unrestrained population expansion Conversely, logistic growth considers resource limitations and a carrying capacity (K) - the maximum sustainable population
Exponential and logistic growth of populations - Khan Academy Logistic growth occurs when a population grows exponentially at first, but then slows As the population’s growth slows, its size begins to level off Logistic growth usually occurs as resources become scarce and competition increases Populations that have logistic growth produce an S-shaped curve
The logistic growth model - Khan Academy The logistic differential equation dN dt=rN (1-N K) describes the situation where a population grows proportionally to its size, but stops growing when it reaches the size of K
Population growth and carrying capacity - Khan Academy A population of harbor seals in Washington state (left) follows logistic growth (right) Growth slows as the population nears carrying capacity (indicated by the red dashed horizontal line) The number of seals (indicated by orange dots) fluctuates above and below this maximum population size