Step by step
The question
Question: A substance has a half-life of 5 years.
How much of 80 g is left after 20 years?
1 Count the half-lives
Every 5 years, half is left.
Half means times 1/2.
every 5 years: × 12
How many half-lives in 20 years?
20 divided by 5: 4.
half-lives = 205 = 4
Careful!
4 half-lives is not divided by 4.
It is halved 4 times, one after another.
Careful: not 80 ÷ 4 = 20 g ✗
2 Halve it that many times
A = the start times (1/2) to the power 4.
A = 80 × (12)4
(1/2) to the power 4 is 1/16.
(12)4 = 116
80 times 1/16 is 80/16.
A = 8016
80 divided by 16 is 5 g.
A = 5 g
3 Check
Let's check, half-life by half-life.
Every 5 years, we halve it.
After 20 years we get 5 g again.
It works!
after 20 years: 5 g
Let's look back.
First: count the half-lives.
Then: halve it that many times.
Last: check.
Answer
A = 5 g