### Exponential decay

Exponential graphs are important in several aspects of science. Exponential decay is seen in the discharge of

capacitors and in radioactive decay. At first sight an exponential relation between two quantities is hard to understand. But imagine, if a bucket has a hole in the bottom through which the water drains out the level of the water will go down exponentially. The shape of the graph of an exponential decrease is like this:

The video at the bottom of the page explains an example of exponential decay.

### Exponential increase

The term exponential increase is often misused to simply describe something increasing rapidly. One nearly exponential increase suffered by the world recently has been the start of the pandemic and the start up of new strains within the pandemic.

To be strictly exponential the increase should be regular, for example doubling in a fixed period of time. For example that might be:

Day 1          1 infection

Day 2          2 infection

Day 3          4 infection

Day 4          8 infection

Day 5          10 infection

To begin with this does not seem very dramatic, but try working out how many there will be after one month on day 30! That

would be 536,870,912.

In reality the increase soon stops being truly exponential (fortunately) because of human actions. An exponential increase graph looks like this:

### Exponential change

Other pages related to graphs and general physics ideas are: