Step by step
The question
Question: M = 400(0.5)ᵈ is the amount of medicine left, in milligrams, d days from now.
What does 0.5 mean?
We write the equation big, so we can label it.
1 What the letters mean
M is the amount of medicine left, in milligrams.
d is the number of days.
It is the small raised number, the power: how many times we multiply by 0.5.
2 Make a small table
To see what each number does, we try a few days: 0, 1 and 2.
0 is where it starts.
d = 0: no days have passed, so we multiply by 0.5 zero times.
That is why 0.5 to the power 0 is 1.
400 times 1 is 400.
d = 1: 0.5 to the power 1 is just 0.5.
400 times 0.5 is 200.
d = 2: 0.5 squared is 0.5 times 0.5.
400 times 0.5 is 200.
Times 0.5 again: 200 times 0.5 is 100.
Look at the values of M: 400, 200, 100.
Each time d goes up 1, M is multiplied by 0.5.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
400 is M at d = 0: the first number in the table.
So 400 is the amount of medicine left at the start.
0.5 is what we multiply by, once for each day.
That is the power d: it counts the days.
Careful!
0.5 is multiplied, not taken away.
Look at the table: 400, 200, 100.
4 Say it in words
So 0.5 means: the amount of medicine left halves each day.
Times one half is half.
5 Check
Let's check one more step: 200 cut in half is 100: the table at d = 2.
It works!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: say it in words.
Last: check.