## About Exponential Growth (Formula)

Exponential growth is a mathematical concept that describes the growth of a quantity at a fixed percentage rate over time. It is a type of compound interest, where the growth rate is constant and is applied to the new balance each period. The formula for exponential growth is:

**x(t) = x0 × (1 + r) t**

where:

x(t) is the value of the quantity at time t x0 is the initial value of the quantity r is the growth rate (expressed as a decimal) t is the time elapsed (in the same units as the growth rate)

The formula above shows that the value of the quantity increases exponentially over time, as each new value is calculated by multiplying the previous value by (1 + r). This is the key feature of exponential growth, as the rate of growth is proportional to the current value of the quantity, rather than being constant over time.

Exponential growth is a widely applicable concept in many fields, such as finance, biology, and physics. It is used to model the growth of populations, the spread of diseases, the decay of radioactive materials, and many other phenomena. It is an important tool for predicting future trends and making informed decisions based on data.