# 8 Exponential Decay Examples in Real Life

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

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.