Step by step
The question
Question: 200 bacteria double every hour.
How many are there after 5 hours?
1 Find the start and the factor
The start is 200.
Double means times 2.
So the factor is 2.
start: a = 200
factor: b = 2
2 Write the rule
x is the number of hours.
Each hour we multiply by 2 again.
So y = 200 × 2ˣ.
y = 200 × 2x
Careful!
Doubling 5 times is times 2, 5 times over.
Not times 10.
Careful: not 200 × 2 × 5 = 2000 ✗
3 Put in x = 5
After 5 hours, x = 5.
y = 200 × 25
2 to the power 5 is 32.
25 = 32
So we multiply 200 by 32.
= 200 × 32
So it is 6400.
= 6400
4 Check
Let's check hour by hour.
We start at 200, and multiply by 2 each hour.
After 5 hours we get 6400 again.
It works!
after 5 hours: 6400
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 5.
Last: check.
Answer
= 6400