Exponential decay describes the process of reduction in the magnitude or value of a particular quantity at a consistent rate over a period of time. In other words, if a value tends to move towards zero rapidly, it is said to be exhibiting an exponential decay. The concept of exponential decay is being utilized by a variety of fields such as finance, biology, chemistry, physics, ecology, archaeology, etc.
Examples of Exponential Decay
1. Radioactive Decay
Radioactive decay of the isotopes of radioactive elements is a prominent example of exponential decay in real life. Let us assume, if the substance has a half-life of one week, i.e., if the radioactivity of a particular substance reduces to half of its original value on the last day of every passing week, it is said to be exhibiting decay as an exponential function. If a graph of the radioactivity of such a substance is plotted with respect to time, it has a negative slope that reduces gradually and gets flattened at the end, which clearly resembles the exponential decay graph.
2. Reselling Cost of a Car
The reselling cost of a car or any other product deteriorates with every passing year. During the first year, the original cost of the product gets depreciated by a constant percentage and the depreciated new cost of the car is known by the end of the year. During the second year, the newly obtained cost acts as the original cost that gets depreciated with the same constant percentage by the end of the year. The process goes on and on every year. Since the cost reduces gradually at a consistent rate, it clearly represents the exponential decay. The concept of exponential decay can be used by the consumer to get a rough estimation of the most suited time to resell his/her object. If a person has an intention to resell his car or other valuable objects at a good price he/she must keep a record of the deteriorating value of the object.
3. Population Decline
The concept of exponential decay is used to keep a track record of the population of the species that are on the verge of extinction. For instance, if a certain species of birds are getting extinct at a rate of 3% per decade, then the concept of exponential decay can be implemented to the current data, and the year by which the entire species is about to vanish thoroughly can be estimated in advance. This helps the environment engineers compute and take preventive measures to save the species from getting extinct. The decrease in the human population is yet another example of exponential decay in real life.
4. Treatment of Diseases
When a person who is suffering from a bacterial or viral disease visits a doctor to receive treatment, the doctor tends to provide him with certain antibiotic drugs and medicines. These drugs and medicines primarily affect the life of the microorganisms present inside the body responsible for the disease by refraining them to undergo reproduction and killing them. The number of microbes present in the body is reduced, following an exponential pattern. Hence, it is yet another example of exponential decay observed in real life.
5. Consuming a Bag of Candy
Suppose a child is given a bag of candy. He/she wishes to eat the half of candies present in the bag every day. In such a case, exponential decay can be observed easily. For instance, suppose the bag consists of 120 candies. On the first day, the child consumes half of the total candies, i.e., 60 candies. The next day, the child consumes 30 candies. On the third day, he/she eats 15 candies, and so on. If the child continues to follow such a pattern of consuming candies, he/she tends to display an exponential decay in real life. Plotting a graph of the number of candies consumed with respect to the number of days gives a negative slope graph that gradually decreases and gets flattened while reaching the end.
6. Radiocarbon Dating
Radiocarbon dating was discovered by an American physical chemist Willard Libby in 1949, who later won a Nobel Prize for his discovery in 1960. It is used to calculate the approximate date and time when a plant or an animal would have died. It compares the ratio of the two isotopes of carbon present in the organic matter or fossil with the ratio of the same isotopes present in the air. The process of radiocarbon dating highly depends on the radioactive decay of the isotopes of radioactive elements, hence forms a prominent example of exponential decay in real life. Radiocarbon dating also helps the researchers to estimate the time when an ancient artefact was built.
7. Calculating the amount of drug in a person’s body
The concept of exponential decay is also used in calculating the amount of drug remaining in a person’s body after a certain duration of time. Let us say if a person is injected with a certain drug. The initial amount of the drug present in the person’s blood is 250 mg, and it gets dissolved at a rate of 3 mg per hour. Now, if it is required to calculate the amount of drug left in the person’s body after 5 hours, one can simply use the exponential decay function because the drug dissolves consistently at a constant rate. This means that the concept of exponential decay helps doctors and chemists calculate the effectiveness and side effects of a particular medicine.
8. Healing of Wounds
Wounds and bruises take time to heal properly. Interestingly, the healing of wounds and bruises depends on the concept of exponential decay because the size of the wound, during the process of healing, is reduced consistently at a constant rate. This means that if the rate of healing of the wound is known, the time when the wound would get properly healed can be estimated accurately.