Exponential growth/decay equations & usage

• Nov 24th 2011, 08:06 AM
benny92000
Exponential growth/decay equations & usage
In my book I am given the equation A(t) = Aoe^(kt) (for exponential growth) Where t equals time and k is a constant. However, I saw an equation on another site for compounded interest in which k was replaced by r, the rate of interest. When do you use which equation? And what about exponential decay?
• Nov 24th 2011, 10:59 AM
corsica
Re: Exponential growth/decay equations & usage
From your description I would say that both equations are identical. They've merely applied a different nametag to the constant.

If $\displaystyle k>0$ then there is exponential growth. If $\displaystyle k<0$ there is exponential decay (towards zero).
• Nov 24th 2011, 11:20 AM
e^(i*pi)
Re: Exponential growth/decay equations & usage
Quote:

Originally Posted by benny92000
In my book I am given the equation A(t) = Aoe^(kt) (for exponential growth) Where t equals time and k is a constant. However, I saw an equation on another site for compounded interest in which k was replaced by r, the rate of interest. When do you use which equation? And what about exponential decay?

The equations are the same. $\displaystyle r$ and $\displaystyle k$ are constants with dimension 1/TIME. Different fields tend to use different symbols but they all refer to a constant. For example you'll see $\displaystyle \lambda$ used as a decay constant in radioactivity. A good book will define it's symbols immediately before/after introducing them.

Whether it's growth or decay depends whether or not there is a minus sign since the constant in the exponent is usually taken to be a positive constant. If it's there then you have decay, if not then it's growth. Below is an example

Radioactive decay is given by the formula $\displaystyle N = N_0e^{-\lambda t}$ where $\displaystyle N$ is the number of nuclei at any given time, $\displaystyle N_0$ is the initial number of nuclei (when t=0), $\displaystyle \lambda$ is a positive decay constant and $\displaystyle t$ is time