The multiplicative rate of change of a function is an important concept in mathematics. It is used to measure how a function changes over time, and is closely related to the derivative of a function. In this article, we will explore what the multiplicative rate of change is, and provide some examples of this concept in action.

## Definition of Multiplicative Rate of Change

The multiplicative rate of change of a function is the ratio between two points on the graph of the function. It is also known as the relative rate of change or the exponential growth rate. It is used to measure the rate at which a function changes over time.

The multiplicative rate of change is calculated by taking the ratio of the values of the function at two different points in time. The formula is given by:

multiplicative rate of change = (value of function at point 2) / (value of function at point 1).

## Examples of Multiplicative Rate of Change

One example of the multiplicative rate of change is the growth of a population over time. To calculate the multiplicative rate of change, we would take the ratio of the population at two different points in time. For instance, if the population at time 1 was 100 people and the population at time 2 was 200 people, the multiplicative rate of change would be 2.

Another example of the multiplicative rate of change is the rate of growth of an investment over time. To calculate the multiplicative rate of change, we would take the ratio of the value of the investment at two different points in time. For instance, if the value of the investment at time 1 was $100 and the value of the investment at time 2 was $200, the multiplicative rate of change would be 2.

In conclusion, the multiplicative rate of change is a useful concept that can be used to measure how a function changes over time. It is calculated by taking the ratio of the values of the function at two different points in time. Examples of the multiplicative rate of change include the growth of a population over time and the rate of growth of an investment over time.