ACT Preparation / Unit 12 ACT 1122 worked example, 60 to 90 seconds
A Half-Life Problem
The idea
A half-life problem is solved in three steps. First, write A = A₀(1/2)^(t/h), with the time and the half-life in the same unit. Second, substitute what is known. Third, if the time is unknown, divide by A₀, take logs, and solve; if the amount is unknown, evaluate. A whole number of half-lives can be counted directly.
In practice
Worked example: an invented isotope has a half-life of 8 hours. How long until 400 milligrams decays to 50? Divide: 50/400 = 1/8 = (1/2)³, so t/8 = 3, and t = 24 hours, three half-lives. Second: how much of the 400 remains after 12 hours? 400(1/2)^(12/8) = 400(1/2)^1.5, about 141.4 milligrams.
Where people slip
A fraction of a half-life does not remove a matching fraction of the amount: after 12 hours, one and a half half-lives, about 141 milligrams remain, not the 150 a straight line would suggest.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Unlocks
- Nothing yet depends on this.
Something wrong in this lesson? Flag it · Sources for ACT Preparation