# Rather simple question... (What is "time constant"?)

• Oct 30th 2008, 01:06 PM
natashabu
Rather simple question... (What is "time constant"?)
So a math question says "An unspecified quantity of a radioactive element is stored in a safe vault in the year 2000. Six years later, we find there is only half the amount there was originally." one of the subquestions is to find the "TIME CONSTANT..."

I know how to do these types of questions (radioactive decay and all that jazz) so I don't need the actual answer or any explanations... rather I just need to know what exactly time constant IS. Is it the original quantity when time is zero? Or is it the half-life? Or what? How is it defined?

Thanks :)
• Oct 30th 2008, 01:56 PM
skeeter
the following general equation models exponential growth or decay (base e) ...

\$\displaystyle A = A_0 e^{kt}\$

\$\displaystyle A\$ = amount of material present at any time t

\$\displaystyle A_0\$ = amount of material at time t = 0

k is the time constant
• Oct 30th 2008, 02:22 PM
natashabu
Quote:

Originally Posted by skeeter
the following general equation models exponential growth or decay (base e) ...

\$\displaystyle A = A_0 e^{kt}\$

\$\displaystyle A\$ = amount of material present at any time t

\$\displaystyle A_0\$ = amount of material at time t = 0

k is the time constant

Are you sure? I'm pretty certain k is the DECAY constant (because the question asks for both decay constant and time constant)...
• Oct 30th 2008, 03:19 PM
skeeter
not sure ... I do know that k is the time constant when dealing with RC and RL circuits.

here is a wiki link that seems to explain the difference ...

http://en.wikipedia.org/wiki/Exponential_decay