Half-Life Population Growth Formula

Half-Life Model : If H is the half-life of a quantity (the amount of time it takes the quantity be cut in half) and P_o is the initial amount of the quantity then the amount of the quantity present after t units of time is

Formula :

P_t = P_o(12)^tH

Where,

P_t = Quantity remains

P_o = Initial quantity

H = Half-life

t = time

Example :

Lead-209 is a radioactive isotope. It has a half-life of 3.3 hours. Suppose that 40 milligrams of this isotope is created in an experiment,

how much is left after 14 hours? Use the half-life model to solve this problem. P_o = 40 and H = 3.3 , so the half-life model for this problem is:

P_t = 40 (12)^t3.3 , When t = 14 hours

P₁₄ = 40 (12)^143.3 = 2.1

There are 2.1 milligrams of Lead-209 remaining after 14 hours.