Step by step
The question
Question: A substance has a half-life of 2 hours.
How much of 48 g is left after 8 hours?
1 Count the half-lives
Every 2 hours, half is left.
Half means times 1/2.
every 2 hours: × 12
How many half-lives in 8 hours?
8 divided by 2: 4.
half-lives = 82 = 4
Careful!
4 half-lives is not divided by 4.
It is halved 4 times, one after another.
Careful: not 48 ÷ 4 = 12 g ✗
2 Halve it that many times
A = the start times (1/2) to the power 4.
A = 48 × (12)4
(1/2) to the power 4 is 1/16.
(12)4 = 116
48 times 1/16 is 48/16.
A = 4816
48 divided by 16 is 3 g.
A = 3 g
3 Check
Let's check, half-life by half-life.
Every 2 hours, we halve it.
After 8 hours we get 3 g again.
It works!
after 8 hours: 3 g
Let's look back.
First: count the half-lives.
Then: halve it that many times.
Last: check.
Answer
A = 3 g