## Exponential

### Exponential refers to a mathematical function or relationship that involves constant growth or decay

Exponential refers to a mathematical function or relationship that involves constant growth or decay. It is commonly represented by the equation y = ab^x, where “a” is the initial value or starting point, “b” is the base or growth/decay factor, and “x” represents the exponent.

In exponential growth, the base (b) is greater than 1, which causes the function to rapidly increase over time. This is often associated with population growth, compound interest, or the spread of diseases.

For example, let’s say we have an initial population of 100 bacteria, and the bacteria multiply by a factor of 2 every hour. The population growth can be represented by the exponential function y = 100 * 2^x. As time (x) increases, the population will double every hour.

On the other hand, exponential decay occurs when the base (b) is between 0 and 1, causing the function to decrease rapidly over time. This is commonly observed in radioactive decay or the diminishing effect of medication dosage.

For instance, suppose we have 500 grams of a radioactive substance with a decay constant of 0.5. The amount of the substance remaining can be described by the exponential decay function y = 500 * 0.5^x. As time (x) increases, the remaining amount will halve repeatedly.

Exponential functions play a crucial role in various fields such as economics, biology, and physics. They are particularly useful in modeling growth or decay processes when the rate of change is proportional to the current value.

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