Halving
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 7 of 49.
A radioactive substance decays at a steady pace. Its half-life is the time it takes for half of what is left to decay. Take 800 grams with a half-life of one year. After one year 400 grams are left, after two 200, after three 100. Three half-lives multiply the start by (1/2)^3, so 800 × (1/2)^3 = 100.
This is decay with b = 1/2. After t half-lives the amount is the start times (1/2)^t. As with doubling, the exponent counts half-lives, not years: with a half-life of 2 years, 6 years would be 3 half-lives.
Halving never gets the sample to zero. Half of something is always something, so in this model a little is always left, however long you wait.
Challenge
A 640 gram sample of a radioactive substance has a half-life of one day: each day, half of what is left decays. Find the amount A left after 5 days, in grams. On the blank board, first write an A = ... line as the start times a power, then work out its value on the next line.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponentials, Logs & Sequences
1Exponential Functions
Repeated MultiplyingGrowth or DecayDrawing GrowthDrawing DecayRecap: Exponential Functions