- #1
Irishdoug
- 102
- 16
Homework Statement
Show using your expression for \lambda that if at a time t1 the amount is y1, then at a time t1 + ##\lambda## the amount will be ##\frac{y1}{2}##, no matter what t1 is.
Homework Equations
y = y0 ##e^{kt}##
From previous question: half life ##\lambda =-ln2/k##
The Attempt at a Solution
y1 = y0 ##e^{kt1}## so t1 = ##\frac{lny1}{y0k}##
so:
y (t1+## \lambda ##) = y0 e^(k ##\frac{lny1}{y0k}##+ k## \frac{-ln2}{k}##) = y0 e^{ln##\frac{y1}{y0}## +2}
The k's cancel.
-ln2 = ln 1/2
The e and ln cancels
so;
yo * ##\frac{y1}{y0}## * ##\frac{1}{2}## = ##\frac{y1}{2}##
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