Question

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

Answer 1

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.
$A_o$ = Amplitude of smallest detectable wave.
From this we can find R the Richter scale measure of magnitude of earthquake.
$R = log \frac{A}{A_o}$

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
$A = P(1+ \frac{r}{n})^{nt}$
Where P is principal amount , r = rate of interest(decimal) , n is the number of compounding period , t is time.

For