Chapter 6.9, Problem 46E

General relative growth rates Define the relative growth rate of the function f over the time interval T to be the relative change in f over an interval of length T:

$R_T=\frac{f(t+T)-f(t)}{f(t)}.$

Show that for the exponential function y(t) = y₀e^kt, the relative growth rate R_T is constant for any T; that is, choose any T and show that R_T is constant for all t.