$y={y}_{0}{e}^{\lambda t}$

## Model

The model of exponential growth is based on that a stock y (eg. a population) is all the more increased the greater the inventory itself. That in the model with the magnitude of the population continues to increase the growth rate.

## Limitations of the model

The model does not account limiting factors such as only a finite available resources. A model that takes this into account leads to the model of logistic growth.

## Half-life or doubling time T

The half-life or doubling time T is the period in which the stock is doubled or halved.

Exponential growth:

$$T=\frac{ln2}{\lambda}$$

Exponential decay:

$$T=\frac{ln\frac{1}{2}}{\lambda}$$

## Application Examples

Growth of populations

Radioactive decay

Absorption of light

Compound interest