What is exponential decay in real-life situations?

Exponential decay describes how quantities decrease rapidly at first, then slowly over time, like radioactive decay.

In real-life situations, exponential decay can be observed in various contexts. One common example is radioactive decay, where unstable atomic nuclei lose energy by emitting radiation. The rate at which this happens is proportional to the amount of the substance present. For instance, if you have a sample of a radioactive material, it will lose half of its radioactivity over a fixed period known as its half-life. This process continues, with the material losing half of its remaining radioactivity in each subsequent half-life period.

Another example is the cooling of hot objects. According to Newton's Law of Cooling, the rate at which an object cools is proportional to the difference in temperature between the object and its surroundings. So, if you take a hot cup of tea and leave it in a cooler room, it will cool down quickly at first, but the rate of cooling will slow as the temperature difference decreases.

Exponential decay also appears in finance, particularly in the depreciation of assets. For instance, a new car loses its value quickly in the first few years, but the rate of depreciation slows down over time. This is because the value of the car decreases by a fixed percentage each year, rather than a fixed amount.

Understanding exponential decay helps us analyse and predict how different quantities change over time, which is useful in fields ranging from science to economics.