Question

How are exponential growth and decay present in the real world? Give at least 2 examples for exponential growth and 2 examples of exponential decay.

Answer 1

I need help omg

Answer 2

Exponential phenomenon of growth and decay are continuously occurring in our vicinity. We can experience these phenomenons in nature, real world and in different scientific approaches. So one can easily understand the importance of processes of exponential growth and decay due to their occurrence in diversified scenarios like science and technology, real world and even in nature.
When we talk about nature we can witness processes of exponential growth in the form of population growth of human, bacterial growth rate follow the exponential growth, dissemination of viral disease is exponential etc. Exponential population growth is very much important and critical to living world as we all know that current population of world is exceeding the carrying capacity of earth due to its exponential growth which is resulting in severe food crisis, water scarcity and economic fall down of the planet earth. In similar way exponential bacterial growth also have prime importance e.g. exponential growth of pathogenic bacteria may lead towards the severe disease outbreaks in the world like anthrax, cholera, malaria etc. Moreover, exponential growth of food bacteria in food industry may lead towards the food spoilage and food poisoning that further result in different diseases of human being. In the same way viral infection or dissemination of viruses also follow the exponential growth pattern e.g. exponential expansion of different viral diseases like dengue, Aids and others. When we come down to real world and science and technology’s processes of exponential growth often face economic growth which also follows the exponential growth pattern thus the exponential or sudden increase in the Gross Domestic product (GDP) plays an important role in a country’s prosperity. Similarly weapons of mass destruction (nuclear weapons) and nuclear energy is obtained by controlled fission reactions but if these fission reactions become uncontrolled or in other words exponential (in fact in uncontrolled fission reactions production of or increase of neutrons after every fission reaction is exponential i.e. the cause of fission process to trigger) may lead towards the melt down or explosion of an atomic reactor or nuclear power plant as it happened in Chernobyl disaster in Russia.
On the other hand when we talk about examples of exponential decay in nature the first thing that come to our mind is exponential radioactive decay that in how much time a potentially dangerous radioactive substance will finish. For this purpose we often used the term half life the time at which the specific substance has reduced to half of its initial quantity. Exponential Radioactive decay or more specifically half life is a phenomenon of paramount importance in the nature. Like carbon dating can be used to find out the age of a fossil. In carbon dating we measure the half life of isotopes and from this we estimate the age of a fossil. Apart from this it is also important to know the half life of radioactive materials as they are carcinogenic. So if we know the half life of a certain radioactive material present at a certain place possessing potential danger to human and other life forms then one can say with trust that after which time the place where that particular radioactive substance is present will be safe for human and other life forms. Another example is that the half life of a particular isotope simply tells how long it will remain dangerously radioactive. By storing the spent fuel rods on site much of the shorter lived more intense radiation will have decayed before moving it to a long term repository. Exponential decrease of pressure also takes place when we move towards higher altitudes. Due to this exponential decrease in pressure people living at higher altitudes face problems of breathing and elongated cooking time.
When we come towards the exponential decay processes of real world and science and technology we often discuss about the first order chemical reactions in which the reactant (on which the reaction rate depends) decrease or decay exponentially with time. So exponential decay is very much important in a sense that after how much time a potentially hazardous pollutant present in water body will be decayed according to first order chemical kinetics. Similarly charged stored on a capacitor decayed exponentially so we can estimate that for how long charged can be stored on specific capacitor or charge storing body. One of the most important examples of exponential decay in medical science is elimination or metabolism of medicines and drugs from human body. If a drug or medicine stays for longer time period in human body than desired then it may cause poisonous effect in human body.