Algebra 2 · Unit 6 · Topic 6.5
Half-Life, Doubling Time, and Model Limits
A quantity with half-life H > 0 is modeled by A(t) = A₀(1/2)^(t/H).
Definition and explanation
A quantity with half-life H > 0 is modeled by A(t) = A₀(1/2)^(t/H). A doubling-time model uses A(t) = A₀2^(t/T) with T > 0. Both assume the multiplicative behavior remains constant over time.
Worked example
A hypothetical sample starts at 160 units with a half-life of 3 hours. At t = 9 hours, three half-lives have passed, so A = 160(1/2)³ = 20 units. The model halves the amount every 3 hours, not subtracts 80 each time.
Common mistake
Half-life describes a multiplicative pattern, not a constant additive decrease.
Key takeaway
A quantity with half-life H > 0 is modeled by A(t) = A₀(1/2)^(t/H).
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.