# Exponential Growth Calculator

**
Instructions:
**
Use this step-by-step Exponential Growth Calculator with steps to find the function that describe the exponential growth for the given parameters. You need to provide the initial value \(A_0\), increase rate per period (which could be yearly or continuous).

## The Exponential Growth Calculator

Exponential Growth is an algebraic behavior that has many uses in real life, from Finance to Economics, from Social Sciences to Biology. It represents a growth that is compounded every period by a certain rate (or percentage). One way of seeing is that the rate of change is proportional to the size of the function.

It is said that a function \(f(t)\) has an exponential growth behavior if it can be expressed as:

\[f(t) = A_0 (1 + r)^t \]For the above formula, \(r\) corresponds to the growth rate, expressed as a decimal number or as a percentage (they are equivalent). Typically, you will be provided with the compounding growth rate and the initial value \(A_0\), but sometimes you will be provided with information about the function, and you will have to infer the parameters \(r\) and \(A_0\).

For the above exponential growth formula, there is a special case where the rate is compounded continuously, in which case the formula becomes

\[f(t) = A_0 e^{rt} \]Typically, exponential growth functions represent money, but like we mention before, the can represent a variety of phenomena, such as population growth. You can use this exponential function calculator for different types of models, provided that you know the parameters that are required.

Observe that this calculator will also provide you with the graph of the resulting exponential function.

You can also can use this exponential decay calculator for the reverse but analogous exponential behavior, that corresponds to exponential decay.