First Order - Amount Remaining at time '$$t$$'

$$[A]_t = [A]_0 \cdot e^{-k \cdot t} = \frac{[A]_0}{2^N}$$

$$\qquad N = \frac{t}{t_{1/2}}$$

Concept: Calculates the remaining concentration of a reactant undergoing exponential decay after a specific time interval or a given number of half-lives.

Notation:

• $$[A]_t$$ = Reactant concentration at time $$t$$;
• $$[A]_0$$ = Initial concentration;
• $$N$$ = Number of half-lives elapsed;
• $$t$$ = Total time;
• $$t_{1/2}$$ = Half-life period.