# Calculate exponential growth when rate r is changing

1. Dec 4, 2012

### Vodkacannon

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?

2. Dec 4, 2012

### haruspex

It depends on how it increases with t. Is it linear with t? Geometric? Logarithmic? ...

3. Dec 5, 2012

### HallsofIvy

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.