Step by step
The question
Question: B = 250(3)ʰ is the number of bacteria in a dish h hours from now.
What does 250 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 3.
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 3 zero times.
That is why 3 to the power 0 is 1.
250 times 1 is 250.
h = 1: 3 to the power 1 is just 3.
250 times 3 is 750.
h = 2: 3 squared is 3 times 3.
250 times 3 is 750.
Times 3 again: 750 times 3 is 2250.
Look at the values of B: 250, 750, 2250.
Each time h goes up 1, B is multiplied by 3.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
3 is what we multiply by, once for each hour.
That is the power h: it counts the hours.
250 is B at h = 0: the first number in the table.
So 250 is the number of bacteria at the start.
Careful!
250 is not added each hour.
It is the amount at h = 0, before any multiplying.
4 Say it in words
So 250 means: the number of bacteria is 250 at h = 0.
That is the start.
5 Check
Let's check by going back one hour, from h = 1 to h = 0.
To get to h = 1, we multiplied by 3.
To go back, we divide by 3.
750 divided by 3 is 250: the start.
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.