Step by step
The question
Question: W = 1600(0.75)ᵈ is the water left in a pond, in liters, d days from now.
What does 0.75 mean?
We write the equation big, so we can label it.
1 What the letters mean
W is the water left, in liters.
d is the number of days.
It is the small raised number, the power: how many times we multiply by 0.75.
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 0.75 zero times.
That is why 0.75 to the power 0 is 1.
1600 times 1 is 1600.
d = 1: 0.75 to the power 1 is just 0.75.
1600 times 0.75 is 1200.
d = 2: 0.75 squared is 0.75 times 0.75.
1600 times 0.75 is 1200.
Times 0.75 again: 1200 times 0.75 is 900.
Look at the values of W: 1600, 1200, 900.
Each time d goes up 1, W is multiplied by 0.75.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
1600 is W at d = 0: the first number in the table.
So 1600 is the water left at the start.
0.75 is what we multiply by, once for each day.
That is the power d: it counts the days.
4 Write it as a percent
A percent is out of 100: one whole is 100%.
So we multiply by 100.
0.75 times 100 is 75.
So 0.75 is 75%.
75% is what is left.
100% take away 75% is 25%: the part that is lost.
Careful!
75% is the part that is left.
The part that is lost is 25%.
5 Say it in words
So 0.75 means: the water left goes down by 25% each day.
6 Check
Let's check the 25%.
25% is 25/100, that is 0.25.
25% of 1600 is 0.25 times 1600: 400.
1600 minus 400 is 1200: the same as the table at d = 1.
It works!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: write it as a percent.
Then: say it in words.
Last: check.