# What’s the relation between activity and half-life

I’m confused because there are two equations:

1) A=λN

2) A=A0exp^-(λt)

If half-life increases, λ decreases, and A decreases according to 1); but,

If half life increases, λ decreases, hence exp^-(λt) decreases, A should decreases according to 2)

Why is this so? Where went wrong? Thanks!

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Drakkith
Staff Emeritus
If half life increases, λ decreases, hence exp^-(λt) decreases
This doesn't look correct. Given the function $Y=e^{-x}$,
$Y$ should increase if $x$ decreases since $e^{-x}=\frac{1}{e^x}$. Graphing this equation should immediately show you how the function behaves.

1) A=λN

2) A=A0exp^-(λt)
Hmmm. I think the second equation should be $N=N_0e^{-λt}$, where $N$ is the number of nuclides remaining after time $t$.

This doesn't look correct. Given the function $Y=e^{-x}$,
$Y$ should increase if $x$ decreases since $e^{-x}=\frac{1}{e^x}$. Graphing this equation should immediately show you how the function behaves.

Hmmm. I think the second equation should be $N=N_0e^{-λt}$, where $N$ is the number of nuclides remaining after time $t$.