Math  /  Algebra

QuestionA laptop computer is purchased for $1100\$ 1100. After each year, the resale value decreases by 25%25 \%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar. \ \square$

Studdy Solution

STEP 1

What is this asking? If a laptop loses 25% of its value every year, and it starts at $1100\$1100, how much will it be worth after 4 years? Watch out! Don't forget that the laptop loses 25% of its *current* value each year, not 25% of the *original* value!

STEP 2

1. Calculate the multiplier.
2. Apply the multiplier for each year.

STEP 3

Alright, so the laptop loses **25%** of its value each year.
This means it *retains* **100% - 25% = 75%** of its value.
We can write this as a decimal: **0.75**.
This is our **magic multiplier**!

STEP 4

We **start** with a laptop worth $1100\$1100.
After **one year**, it's worth $11000.75=$825 \$1100 \cdot 0.75 = \$825 .

STEP 5

After **two years**, it's worth $8250.75=$618.75 \$825 \cdot 0.75 = \$618.75 .

STEP 6

After **three years**, it's worth $618.750.75=$464.0625 \$618.75 \cdot 0.75 = \$464.0625 .
Getting close!

STEP 7

After **four years**, it's worth $464.06250.75=$348.046875 \$464.0625 \cdot 0.75 = \$348.046875 .

STEP 8

Rounding to the nearest dollar, we get $348\$348.
Boom!

STEP 9

The resale value after 4 years will be approximately $348\$348.

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