Step by step
The question
Question: A car worth $20000 loses 15% of its value each year.
What is it worth after 3 years?
1 Find the start and the factor
The start is $20000.
Each year it loses 15%.
So 85% is left.
85% is 0.85.
That is the factor.
start: a = $20000
100% − 15% = 85% = 0.85
factor: b = 0.85
2 Write the rule
x is the number of years.
Each year we multiply by 0.85 again.
So y = 20000 × 0.85ˣ.
y = 20000 × 0.85x
Careful!
0.15 is the part that is lost.
We multiply by the part that is left: 0.85.
Careful: not b = 0.15 ✗
3 Put in x = 3
After 3 years, x = 3.
y = 20000 × 0.853
0.85 to the power 3 is 0.614125 (with a calculator).
0.853 = 0.614125
So we multiply 20000 by 0.614125.
= 20000 × 0.614125
So it is $12282.50.
= $12282.50
4 Check
Let's check year by year.
We start at $20000, and multiply by 0.85 each year.
After 3 years we get 12282.5 again.
It works!
after 3 years: 12282.5
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 3.
Last: check.
Answer
= $12282.50