I need an example of the practical use of an exponential or logarithmic function.
One of the most widely used exponential functions would be the one used to find compound interest.
For an amount P deposited at an annual rate of interest r for n years, the amount after n years is given by:
Pn = P0*( 1+ r)^n, the total amount as can be seen grows at an exponential rate. The interest is given by the total amount at any time decreased by the initial amount.
A logarithmic function is used to find the value for the time elapsed if the amount present , the rate of interest and the initial amount are given.
Pn = P0*( 1+ r)^n
=> Pn/P0 = (1+r)^n
=> log( Pn/P0) = log ( 1+ r)^n
=> log( Pn/P0) = n* log ( 1+ r)
=> n = log (Pn/P0)/ ln(1+r)
substituting Pn, P0 and r gives us n.