Step by step
The question
Question: A substance has a half-life of 10 years.
How much of 200 mg is left after 30 years?
1 Count the half-lives
Every 10 years, half is left.
Half means times 1/2.
every 10 years: × 12
How many half-lives in 30 years?
30 divided by 10: 3.
half-lives = 3010 = 3
Careful!
3 half-lives is not divided by 3.
It is halved 3 times, one after another.
Careful: not 200 ÷ 3 = 66.666667 mg ✗
2 Halve it that many times
A = the start times (1/2) to the power 3.
A = 200 × (12)3
(1/2) to the power 3 is 1/8.
(12)3 = 18
200 times 1/8 is 200/8.
A = 2008
200 divided by 8 is 25 mg.
A = 25 mg
3 Check
Let's check, half-life by half-life.
Every 10 years, we halve it.
After 30 years we get 25 mg again.
It works!
after 30 years: 25 mg
Let's look back.
First: count the half-lives.
Then: halve it that many times.
Last: check.
Answer
A = 25 mg