Step by step
The question
Question: 80 mg of a medicine halves every hour.
How much is left after 3 hours?
1 Find the start and the factor
The start is 80.
Half means times 1/2.
So the factor is 1/2.
start: a = 80
factor: b = 12
2 Write the rule
x is the number of hours.
Each hour we multiply by 1/2 again.
So y = 80 × (1/2)ˣ.
y = 80 × (12)x
Careful!
Each hour it halves what is LEFT, not the start.
Careful: not 80 − 3 × 40 ✗
3 Put in x = 3
After 3 hours, x = 3.
y = 80 × (12)3
(1/2) to the power 3 is 1/8.
(12)3 = 18
So we multiply 80 by 1/8.
= 80 × 18
So it is 10.
= 10
4 Check
Let's check hour by hour.
We start at 80, and multiply by 1/2 each hour.
After 3 hours we get 10 again.
It works!
after 3 hours: 10
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 3.
Last: check.
Answer
= 10