Step by step
The question
Question: C = 900(1.5)ʷ is the number of cells in a sample w weeks from now.
What does 1.5 mean?
We write the equation big, so we can label it.
1 What the letters mean
C is the number of cells.
w is the number of weeks.
It is the small raised number, the power: how many times we multiply by 1.5.
2 Make a small table
To see what each number does, we try a few weeks: 0, 1 and 2.
0 is where it starts.
w = 0: no weeks have passed, so we multiply by 1.5 zero times.
That is why 1.5 to the power 0 is 1.
900 times 1 is 900.
w = 1: 1.5 to the power 1 is just 1.5.
900 times 1.5 is 1350.
w = 2: 1.5 squared is 1.5 times 1.5.
900 times 1.5 is 1350.
Times 1.5 again: 1350 times 1.5 is 2025.
Look at the values of C: 900, 1350, 2025.
Each time w goes up 1, C is multiplied by 1.5.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
900 is C at w = 0: the first number in the table.
So 900 is the number of cells at the start.
1.5 is what we multiply by, once for each week.
That is the power w: it counts the weeks.
4 Write it as a percent
A percent is out of 100: one whole is 100%.
So we multiply by 100.
1.5 times 100 is 150.
So 1.5 is 150%.
150% is all of it, 100%, plus 50% more.
Careful!
150% is the new amount: the 100% it had, plus 50%.
The growth is only the part above 100%: 50%.
5 Say it in words
So 1.5 means: the number of cells goes up by 50% each week.
6 Check
Let's check the 50%.
50% is 50/100, that is 0.5.
50% of 900 is 0.5 times 900: 450.
900 plus 450 is 1350: the same as the table at w = 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.