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Exponential Decay: Half-Life Formula
Understand what half-life means, learn the half-life formula, and practice finding remaining amounts or the half-life itself from real data.
What You'll Learn
Half-life is the fixed amount of time it takes for a decaying quantity to drop to half of its current value, no matter when you start counting.
The half-life formula is N(t) equals N naught times one half raised to the power t over T, where T is the half-life.
Half-life connects to the decay rate constant k through the equation T equals natural log of 2 divided by k.
Solving for time or for the half-life itself usually requires logarithms once the exponential equation is set up.
A common mistake is mixing up the sign or placement of the exponent, so always check that plugging in t equals T gives exactly half the starting amount.
What You'll Practice
1
Creating decay tables to track substance amounts over multiple half-life periods
2
Writing exponential equations from word problem contexts
3
Solving for time using logarithms when the decayed amount is known
4
Calculating remaining substance after non-whole number periods
Why This Matters
Half-life calculations are essential in nuclear physics, medicine, and archaeology. You'll use these exponential decay skills to understand carbon dating, medical radiation treatments, and nuclear safetyplus they build your foundation for calculus and advanced science courses.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Half-Life
Exponential Decay
Logarithms
Word Problems
Exponential Functions
Radioactive Decay
Solving Equations
OH Curriculum Aligned