Decay Formula Problem

Question

The half life of a certain isotope is 5.5 years. If there were 20 grams of one such isotope left after 22 years, what was it's original weight?

I understand I will be using the formula : y= a(1-r)^t,

but first must identify the variables.

t=22/5.5 t=4

r=0.5 This is where my question is (I am not looking to solve it!!)!

Where does this rate of 0.5 come from, given this information.

If I can determine how this variable is reached, I can easily solve as 320 grams.

Answer 1

Hello, Brian,

The equation for half life can be written as:

wfere N(t) is the amount left of the initial quantity N₀, with a half life of t_1/2 after t (both in years).

The (1/2) is the amount lost (50% or half-life) raised to the number of half lives (t/t_1/2). In your equation this is represented as (1- 0.5), instead of 1/2 or 0.5. I don't know why, but perhaps to confuse us?

I hope this helps,

Bob