Step by step
The question
Question: A substance has a half-life of 3 days.
How much of 64 g is left after 9 days?
1 Count the half-lives
Every 3 days, half is left.
Half means times 1/2.
every 3 days: × 12
How many half-lives in 9 days?
9 divided by 3: 3.
half-lives = 93 = 3
Careful!
3 half-lives is not divided by 3.
It is halved 3 times, one after another.
Careful: not 64 ÷ 3 = 21.333333 g ✗
2 Halve it that many times
A = the start times (1/2) to the power 3.
A = 64 × (12)3
(1/2) to the power 3 is 1/8.
(12)3 = 18
64 times 1/8 is 64/8.
A = 648
64 divided by 8 is 8 g.
A = 8 g
3 Check
Let's check, half-life by half-life.
Every 3 days, we halve it.
After 9 days we get 8 g again.
It works!
after 9 days: 8 g
Let's look back.
First: count the half-lives.
Then: halve it that many times.
Last: check.
Answer
A = 8 g