What is the multiplicative rate of change of the function?

The multiplicative rate of change of a function is a measure of how much the function changes when its input variable changes by a certain factor. It is calculated as the ratio of the output values of the function for two different input values that differ by the factor.

For example, if a function f(x) has an output value of 10 when x=1 and an output value of 20 when x=2, then the multiplicative rate of change of the function between x=1 and x=2 is:

20/10 = 2

This means that the output of the function doubled when the input variable was multiplied by 2.

The multiplicative rate of change of a function is useful for analyzing exponential growth or decay, as well as for calculating compound interest and other financial investments that grow or decline at a constant rate. It is also important in scientific fields such as physics, where it is used to calculate rates of change for physical quantities like speed, acceleration, and force.