Letโs say the population of an area increases by some per cent every year or the temperature of a place decreases by some degree celsius annually; these problems are identified as Exponential Growth and Exponential Decay.

These two terms not only define the situation but also helps in better prediction of the future.

## Key Takeaways

- Exponential growth is when a quantity increases rapidly at an accelerating rate over time. In contrast, exponential decay refers to a situation where a quantity decreases rapidly at a decelerating rate over time.
- Exponential growth occurs when there is a constant positive rate of change in a quantity. In contrast, exponential decay occurs when there is a constant negative rate of change in a quantity.
- Exponential growth and decay have many real-world applications, including population growth, radioactive decay, and the spread of diseases.

**Exponential Growth vs Exponential Decay**

When a quantity increases over time, it is said to be experiencing exponential growth. An example of exponential growth is compound interest. While, when a quantity decreases over time, it is said to be experiencing exponential decay. An illustration of exponential decay is radioactive decay.

Exponential growth signifies Growth in quantity with time. It draws a curve formed when some value increases at a specific rate. The graph becomes a curve in increasing order, meaning the growth in something over time.

Exponential decay means when a quantity or a value decreases at a rate proportional to its current value. The process denotes a negative curve and retardation towards the X or Y-axis. The power would be represented with a negative sign.

It consists of the decay constant and concepts of half-life.

**Comparison Table**

Parameters Of Comparison | Exponential Growth | Exponential Decay |
---|---|---|

Definition | Exponential growth denotes an increase in quantity with time. | The exponential decay represents a decrease in quantity with time. |

Graph | The graph points far or not close to the axes since it elevates with time. | The graph will be close to axes or can even intersect or touch it. |

Equation | If we say a value has some positive power, it denotes exponential growth. | If we represent an equation with power holding a negative sign, itโll mean decay. |

concepts | Concepts like compound returns exist. | Concepts like Half-life exists. |

**What is Exponential Growth?**

Often we see things that take place with time, like the consumption of food, buying of cars and vehicles, and many more. We notice that things are increasing day by day, resulting in crowding. Also, if we see the population stats of countries, we often see a pattern.

We notice a way that how a country is experiencing an increase.

Those things which increase with time, we say, growth. And if they follow a pattern, we see exponential growth. Exponential Growth means the acceleration in quantity over some time. It occurs when a quantityโs instantaneous rate of change (delta โ) with time is proportional to quantity.

Letโs understand with an example. A cat species rises exponentially every passing year, starting with 2 in the first year, 4 in the second year, 16 in the third year, and so on. Then we can conclude that in the 4th year, the quantity will be 256 or an increase of 2% yearly.

In terms of finance, compound returns cause exponential growth. The compound method is one of the most powerful methods in this sector. This method elevates rapidly with time, starting with a smaller investment.

A firm can analyse while having the exponential graphs handy and which are easy to understand. This makes it better to take decisions effectively.

**What is Exponential Decay?**

When the value decreases concerning time, it comes under Exponential Decay. It follows a pattern, a formula with a decay constant that decreases with values. If we see a formula, it will look like dN/dt = โ ฮปN.

Here N means quantity, lambda is a positive rate known as the exponential decay constant, and the ratio depicts the Quantity concerning time. The other solution will give terms like decay constant, disintegration is constant, rate constant, or transformation constant.

The curve made after putting values in the formula will retard and move around axes. It can either remain parallel to the axes, touch them, or even intersect to go in a negative direction.

A concept arises concerning decay constant, half-life. Itโs depicted by a formula that consists of a pollution constant. Itโs a characteristic of exponential decay. Itโs the time required for decaying N(quantity) to fall to one-half of its original value. A symbol t denotes it with a subscript of 1/2.

Also, concepts like decaying via two or more different processes simultaneously exist. They are also known as decay modes, channels, or routes.

**Main Differences Between Exponential Growth and Exponential Decay**

- Exponential growth signifies growth or increases in values over some time, while decay denotes retardation in matters.
- The growth graph elevates and can move far from axes but doesnโt touch, while the decay graph can either be parallel and close, touch the axes, or even intersect.
- A population increases with a specific percentage is an example of exponential growth, while a decrease in temperature with every passing year by a rate is exponential decay.
- Compound returns give rise to exponential growth, while thereโs nothing like decay.
- If we take a specific equation whose power is taken positively, itโll rise with an increase in values, while if we take a negative value, itโll decrease with an increase in value.

**References**

- https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1540-6261.2009.01518.x
- https://www.sciencedirect.com/science/article/pii/S0006349576856603

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.