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### Course: AP®︎/College Environmental science>Unit 2

Lesson 2: Population growth

# Exponential and logistic growth in populations

Rabbit populations grow exponentially when not limited by resources, space, or predators. 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. Created by Sal Khan.

## Want to join the conversation?

• Uhh, there are no questions I see. But (this will be about exponential growth) what if a community of 30 rabbits doesn't reproduce at all but rabbits from all over the world join this community and there's a pattern: the first 5 years the community grows 29% a year for 5 years, the next five years, the population grows only 5% per year, next 2 years population decreases 2% a month then it restarts that cycle. (remember all of the additions are not reproductions). Would this still be considered exponential growth if the whole population dies off in 400 years
• Whether the change in population is caused by reproduction or rabbits from elsewhere joining, the mathematical relationship is the same. The 29% a year for five years and so on definitely indicate an exponential pattern.

I made a computer program that calculates the number of rabbits in a given year according to the pattern you provided, if you'd like to see that: https://www.khanacademy.org/computer-programming/bio-problem/4647796705640448

It appears that the population would not reach zero after 400 years, if that was what you were thinking.
• shouldn't the rate of death included in this calculation?
• Death rate is part of the calculation. Growth rate equals births minus deaths.
• can someone explain the p(n) part pls
• P(n) is basically an ideal gross Growth Rate for a species. By substituting n to be the amount of period (In this video it is 120 month), you can achieve an expected result of that amount of species after that period of time. Of course, in real life there are a lot more factor and isn't as simple as P(n) = 1000 * (1.1)^n, but this gives us a rough amount.
• what is or mean the carrying capacity
• The limit to the number of organisms a region can support.
• Does the population stay the same after they reach compacity?
• If you mean capacity (you typed compacity), then no. The population cycles, meaning it goes above then below the capacity, like a sine function cycling around its midline. This is mainly due to resource availability.
• At I saw this kind of table in Algebra 2 with a similar way of solving it.
• I've also seen a lot of problems like this in Algebra 1. Sal is basically showing us an exponential growth problem. Math can correlate heavily with science a lot of the time.
(1 vote)
• Is ❝Malthusian Limit❞ fluctuated by many man made cases like war, unemployment and so on? Are these right that impose to maintain family planing and sterilization both male and female, contribute to reduce high population growth?
• The Malthusian limit is based upon his original theory that the production of food will grow at a linear pace (which was proved wrong), while the human population will grow exponentially, which will inevitably lead to famine. However, this Malthusian limit is solely based upon the maximum amount of sustenance that the human population can produce, not war or unemployment, although those can be important factors in population growth. As for the argument of family planning and sterilization, I cannot speak for everybody, but I strongly believe that limiting the growth of the human population is vital if we seek to preserve the biosphere and ourselves from destruction.
• Isn't the appropriate model for population growth a sigmoidal function?
• Sal shows that at .