# Understanding Exponential Growth: Definition, Formula, and Real-Life Examples

![Exponential Growth](https://www.investopedia.com/thmb/jrCj2c3HhHiAVLs7wXVlTWKjHQo=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/exponential-growth.asp-final-ac33a62dba234cd7b19f97eb40ca10e3.jpg)

*— Investopedia / Jake Shi*

## What Is Exponential Growth?

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. The formula for exponential growth is V = S x (1+R), where S is the starting value, R is the interest rate, T is the number of periods that have elapsed, and V is the current value.  
  
To demonstrate exponential growth, suppose a population of mice rises exponentially by a factor of two every year, starting with two in the first year, then four in the second year, eight in the third year, 16 in the fourth year, and so on. In this case, the population is growing by a factor of two each year. If the mice instead gave birth to four pups in the first year, you would have four, then 16, then 64, then 256.

Exponential growth (which is multiplicative) can be contrasted with linear growth (which is additive) and geometric growth (which is raised to a power).

### Key Takeaways

*   Exponential growth results in rapid increases over time, forming the curve of an exponential function.
*   Compounding interest in finance creates exponential growth, significantly boosting investment returns.
*   In exponential growth, the current value is determined by raising the growth rate to the power of elapsed periods.
*   Exponential growth contrasts with linear growth, which adds a constant amount, while exponential growth uses a multiplier.
*   Real-life examples of exponential growth include population growth, compounding interest, and the spread of diseases.  
    

## Exponential Growth in Finance Explained

In finance, [compound returns](https://www.investopedia.com/terms/c/compound.asp) lead to exponential growth, allowing investors to build significant sums from small initial amounts. Savings accounts with [compound interest](https://www.investopedia.com/terms/c/compoundinterest.asp) rates demonstrate this growth pattern.

### Applications of Exponential Growth

Assume you deposit $1,000 in an account that earns a guaranteed 10% rate of interest. If the account carries a simple [interest rate](https://www.investopedia.com/terms/i/interestrate.asp), you will earn $100 per year. The amount of interest paid will not change as long as no additional deposits are made. You will always earn $100 each year.

If the account carries a compound interest rate, however, you will earn interest on the cumulative account total. Each year, the lender will apply the interest rate not to the initial deposit but to the sum of the initial deposit and any interest previously paid.

In the first year, you earn 10% or $100. In the second year, 10% is applied to $1,100, which gives you $110. Each year, the interest grows, creating exponential growth. After 30 years, without more deposits, your account would be worth $17,449.40.

## Calculating Exponential Growth: The Formula

On a chart, exponential growth starts slowly and stays flat initially, then rises quickly to look nearly vertical, as per the formula:

$V=S\times(1+R)^T$

To find the current value, V, multiply the starting value, S, by (1+R) raised to T, where R is the interest rate and T is the number of periods.

## Critical Insights and Limitations of Exponential Growth

While exponential growth is often used in financial modeling, the reality is often more complicated. Exponential growth suits savings accounts where the interest rate is stable and guaranteed. In most investments, this is not the case. For instance, [stock market](https://www.investopedia.com/terms/s/stockmarket.asp) returns are generally linear and do not smoothly follow long-term averages from year to year.

Other methods of predicting long-term returns, such as the [Monte Carlo simulation](https://www.investopedia.com/terms/m/montecarlosimulation.asp), which uses [probability distributions](https://www.investopedia.com/terms/p/probabilitydistribution.asp) to determine the likelihood of different potential outcomes, have seen increasing popularity. Exponential growth models are more useful to predict investment returns when the rate of growth is steady.

## What Are Examples of Exponential Growth?

Common examples of exponential growth in real-life scenarios include the growth of cells, the returns from compounding interest from an asset, and the spread of a disease during a pandemic.

## Is Exponential Growth the Fastest Type of Growth?

No, it’s not. There are faster growth models, such as factorial growth, which uses a larger number for multiplying with every new repetition. Exponential growth uses the same number for every new repetition.

## What Is the Difference Between Linear Growth and Exponential Growth?

Linear growth happens at the same rate of change. Every increase in X would bring about the same increase in Y. It is constant. With exponential growth there is a constant multiplier, so the growth rate is changing.

## The Bottom Line

Exponential growth illustrates the power of compound interest, leading to significant increases over time and underscoring the importance of early investing. The formula for calculating exponential growth is V = S x ( 1 + R ), where the starting value is (S), the interest rate (R), and time is (T).

Savings accounts, interest-earning investments, and populations grow exponentially over time because the growth is multiplicative. Stocks generally grow linearly, so their growth is slower than instruments with compounding interest rates.

> **Article Sources**
>
> 1.  U.S. Securities and Exchange Commission. "[Compound Interest Calculator](https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator)."
>     
> 2.  Columbia University. "[Exponential Growth](https://ccnmtl.columbia.edu/projects/biology/lecture1/expogrow.html)."
>     
> 3.  National Institutes of Health: National Library of Medicine. "[Exploring the Growth of COVID‐19 Cases Using Exponential Modelling Across 42 Countries and Predicting Signs of Early Containment Using Machine Learning](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7436699/)."