## Calculate exponential growth when rate r is changing

The formula f(t) = I(1 + r)t gives the value of something after it has grown for t years, at rate r, with an initial value I.

What if the growth rate r is continuously increasing?
What is the formula now?
Does it relate somehow to xx?
 Recognitions: Homework Help Science Advisor It depends on how it increases with t. Is it linear with t? Geometric? Logarithmic? ...
 Recognitions: Gold Member Science Advisor Staff Emeritus It is, of course, $f(t)= I(1+ r(t))^t$. And, yes, that has similar properties to $x^x$, especially if r(t) is linear.