Step by step
The question
Question: A bike worth $800 loses 25% of its value each year.
What is it worth after 2 years?
1 Find the start and the factor
The start is $800.
Each year it loses 25%.
So 75% is left.
75% is 0.75.
That is the factor.
start: a = $800
100% − 25% = 75% = 0.75
factor: b = 0.75
2 Write the rule
x is the number of years.
Each year we multiply by 0.75 again.
So y = 800 × 0.75ˣ.
y = 800 × 0.75x
Careful!
0.25 is the part that is lost.
We multiply by the part that is left: 0.75.
Careful: not b = 0.25 ✗
3 Put in x = 2
After 2 years, x = 2.
y = 800 × 0.752
0.75 to the power 2 is 0.5625.
0.752 = 0.5625
So we multiply 800 by 0.5625.
= 800 × 0.5625
So it is $450.
= $450
4 Check
Let's check year by year.
We start at $800, and multiply by 0.75 each year.
After 2 years we get 450 again.
It works!
after 2 years: 450
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 2.
Last: check.
Answer
= $450