**Relationship Between Response Time and Half-Life**

Response time is similar to the concept of a half-life; the time
required to reduce some material to one-half of its starting value,
when it is lost by some kind of draining or loss process. Half-life
is commonly used in reference to the decay of radioactive isotopes,
but it also applies to other processes. For instance, if we eliminate
the faucet from out bathtub model, we have reservoir with a single
outflow and that outflow rate depends on the amount of material in
the reservoir, just like radioactive decay. So, when you are finished
with your bath and you pull the plug, you might think about the
half-life of water in your tub. Recall that one way of defining the
response time is the amount of time it takes to reduce the initial
imbalance in a reservoir by 63%. In the case of the tub draining with
no inflow, the steady state is effectively when there is no water in
the tub, so the response time is the length of time required to drain
63% of the initial amount. The half-life is clearly smaller than the
response time, and in fact, it can be shown that the half life is
0.693 times the response time.

RETURN TO MAIN PAGE

RETURN TO CONTENTS OF SECTION ON
MODELING

CONTINUE TO NEXT SECTION ON MODELING