Step by step
The question
Question: A van is worth $24000. Its value goes down 18% each year.
What is it worth after 3 years?
1 Find the start and the factor
The start is $24000.
Each year it loses 18%.
100% take away 18% is 82%: that is what is left.
82% is 82/100: 0.82.
That is the factor.
2 Write the rule
x is the number of years.
Each year we multiply by 0.82 again.
So y = 24000 × 0.82ˣ.
Careful!
0.18 is the part that is lost.
We multiply by the part that is left: 0.82.
3 Put in x = 3
After 3 years, x = 3.
0.82 to the power 3 is 0.551368 (with a calculator).
So we multiply 24000 by 0.551368.
That is 13232.832.
Money is rounded to cents: about $13232.83.
4 Check
Let's check year by year.
We start at $24000, and multiply by 0.82 each year.
After 3 years we get 13232.832 again.
It works!
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 3.
Last: check.