The exponential decay formula related to half-life is used to describe processes where the quantity of a substance decreases over time at a rate proportional to its current value. It is given by:

$N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$

Where:

• $N(t)$ is the quantity of the substance at time $t$,
• $N_0$ is the initial quantity of the substance,
• $T_{1/2}$ is the half-life, the time it takes for half of the substance to decay,
• $t$ is the elapsed time.

This formula shows how the amount of a substance decreases by half every $T_{1/2}$ time units.

Breakdown:

1. Initial quantity: You start with $N_0$.
2. Time effect: After each interval of the half-life $T_{1/2}$, the amount is halved.
3. Exponential decay: The exponent $\frac{t}{T_{1/2}}$ represents how many half-lives have passed.

Do you have any questions or need further details?

Related Questions:

1. How do you calculate the half-life from a decay rate?
2. What is the difference between exponential decay and linear decay?
3. Can half-life be applied to things other than radioactive decay?
4. How does temperature affect the half-life of chemical reactions?
5. What is the significance of the decay constant in the half-life formula?

Tip: For radioactive decay, the half-life is constant and independent of the initial amount of the substance.