# Exponential growth calculator

# Exponential growth

Exponential growth is a mathematical concept that describes a quantity that increases at a constant relative rate over time. In other words, the rate of increase of a quantity is proportional to its current value. The formula for exponential growth is:

**y = a * (1 + r)^t**

**where:**

- y is the final value of the quantity
- a is the initial value of the quantity
- r is the growth rate as a decimal (e.g. 0.05 for 5%)
- t is the time elapsed

For example, suppose you invest $1,000 in a bank account that pays an annual interest rate of 5%. After one year, your account balance would be:

**y = 1000 * (1 + 0.05)^1 = 1050**

After two years, your balance would be:

**y = 1000 * (1 + 0.05)^2 = 1102.50**

As you can see, the balance is growing at a faster rate as time goes on, due to the compounding effect of the interest. Exponential growth is a common phenomenon in many fields, including finance, biology, and physics.