Step by step
The question
Question: A phone worth $600 loses 30% of its value each year.
What is it worth after 2 years?
1 Find the start and the factor
The start is $600.
Each year it loses 30%.
So 70% is left.
70% is 0.7.
That is the factor.
start: a = $600
100% − 30% = 70% = 0.7
factor: b = 0.7
2 Write the rule
x is the number of years.
Each year we multiply by 0.7 again.
So y = 600 × 0.7ˣ.
y = 600 × 0.7x
Careful!
0.3 is the part that is lost.
We multiply by the part that is left: 0.7.
Careful: not b = 0.3 ✗
3 Put in x = 2
After 2 years, x = 2.
y = 600 × 0.72
0.7 to the power 2 is 0.49.
0.72 = 0.49
So we multiply 600 by 0.49.
= 600 × 0.49
So it is $294.
= $294
4 Check
Let's check year by year.
We start at $600, and multiply by 0.7 each year.
After 2 years we get 294 again.
It works!
after 2 years: 294
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 2.
Last: check.
Answer
= $294