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A computer is worth $400 when it is new. After each year it is worth half what it was the previous year. What will its worth be after 4 years? Round your answer to the nearest dollar.

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Answer:

The computer would be worth $25 after 4 years.

General Formulas and Concepts:
Algebra II

Exponential Function Formula: [tex]\displaystyle y = a(b)^x[/tex]

  • a is the initial amount
  • b is the ratio
  • x is the amount of time

Step-by-step explanation:

Step 1: Define

Identify given.

a = $400

b = 0.5

x = 4 years

Step 2: Find

  1. [Exponential Function Formula] Substitute in variables:
    [tex]\displaystyle y = 400 \bigg( \frac{1}{2} \bigg) ^4[/tex]
  2. Evaluate:
    [tex]y = 25[/tex]

∴ the computer's depreciated value over 4 years would sum up to $25.

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Topic: Algebra II

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