How can exponential and logarithmic functions be created to use in real world situations?

In realistic world there are so many examples which use exponential and logarithmic functions.

Use of Logarithmic function
We can find use of logarithmic function in measuring earthquake (Richter Scale) , the brightness of stars , and chemistry(pH balance , measure of acidity and alkalinity)

For example:
In Richter Scale , a logarithmic function that is used to measure the magnitude of earthquake.
If A = measure of amplitude of earthquake wave.
= Amplitude of smallest detectable wave.
From this we can find R the Richter scale measure of magnitude of earthquake.


Use of Exponential Function:

Exponential function may use in finding compound interest , population growth , radioactivity decay , etc.

For example :
As we know the formula for compound interest is

Where P is principal amount , r = rate of interest(decimal) , n is the number of compounding period , t is time.

For

For range i think it’s area