Step by step
The question
Question: B = 300(2)ʰ is the number of bacteria in a dish h hours from now.
What does 2 mean?
We write the equation big, so we can label it.
1 What the letters mean
B is the number of bacteria.
h is the number of hours.
It is the small raised number, the power: how many times we multiply by 2.
2 Make a small table
To see what each number does, we try a few hours: 0, 1 and 2.
0 is where it starts.
h = 0: no hours have passed, so we multiply by 2 zero times.
That is why 2 to the power 0 is 1.
300 times 1 is 300.
h = 1: 2 to the power 1 is just 2.
300 times 2 is 600.
h = 2: 2 squared is 2 times 2.
300 times 2 is 600.
Times 2 again: 600 times 2 is 1200.
Look at the values of B: 300, 600, 1200.
Each time h goes up 1, B is multiplied by 2.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
300 is B at h = 0: the first number in the table.
So 300 is the number of bacteria at the start.
2 is what we multiply by, once for each hour.
That is the power h: it counts the hours.
Careful!
2 is multiplied, not added.
Look at the table: 300, 600, 1200.
4 Say it in words
So 2 means: the number of bacteria doubles each hour.
Times 2 is double.
5 Check
Let's check one more step: 600 times 2 is 1200: the table at h = 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.