Half-Life
High School
Definition
How long it takes an entity that's decaying exponentially to diminish by half. Half-life is usually used in physics to look at the stability of atoms or radioactive decay. It is constant over an exponentially decaying entity's lifetime.
Worked examples
\(A(t) = 100 \cdot \left(\frac{1}{2}\right)^{t/5}\)
If the half-life is 5 years, the amount halves every 5 years: \(A(5) = 50\), \(A(10) = 25\), \(A(15) = 12.5\).
\(50 = 200 \cdot \left(\frac{1}{2}\right)^{t/8}\)
Starting with 200 units and half-life 8 hours, solve for when 50 units remain: \(t = 16\) hours (two half-lives).
Common mistakes
- \(A(t) = A_0 - \frac{A_0}{2} \cdot t\) → \(A(t) = A_0 \cdot \left(\frac{1}{2}\right)^{t/h}\) Half-life decay is exponential, not linear; the amount halves by proportion, not by a constant subtraction.
- After two half-lives, nothing remains. → After two half-lives, \(\frac{1}{4}\) of the original amount remains. Each half-life cuts the current amount in half; it never reaches zero in finite time.
- Half-life changes as the substance decays. → Half-life is constant throughout the decay process. The definition states half-life is constant; it does not depend on how much remains.
Where you'll use it next
You'll use half-life when modeling exponential decay in calculus, studying radioactive isotopes in chemistry and physics, analyzing drug concentration in biology, and solving real-world decay problems in applied math.
Found in 1 StudyPug lesson
Exponential decay: Half-life
12th Grade12thGrade 12 Math
In the field of nuclear physics, half-life refers to the amount of time required for radioactive substances to decay into half. In this lesson, we will work on word questions about exponential decay of radioactive substances.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026