# How to Calculate Instantaneous Decay

If I want to calculate the number of moles/sec decayed of a substance, and I know the number of moles of isotope and the half life, would I then use the following?

$$N/s=N_0e^{1/\tau_{1/2}}$$

Where $N/s$ is the number of moles of instantaneous decay, $N_0$ is the number of moles, $e$ is Euler's number, and $\tau_{1/2}$ is the half lives per second.

$$N = N_0 e^{-t/\tau}$$
where $t$ is the amount of time passed since you had $N_0$ moles of the undecayed substance and $\tau$ is the average lifetime of the decaying substance ($\tau_{1/2} = \tau\ln2$). Take a derivative to get the rate of decay.
$$\frac{dN}{dt} = -\frac{N_0}{\tau} e^{-t/\tau}$$