Math Problem Statement

Suppose a company's computer equipment is decreasing in value according to the function y=4000(0.87)^x. In the equation, x represents the number of years that have elapsed since the equipment was purchased and y represents the value in dollars. What was the value 5 years after the computer equipment was purchased? Round your answer to the nearest dollar.

Solution

To find the value of the computer equipment 5 years after it was purchased, we can substitute x=5x = 5 into the given equation:

y=4000(0.87)xy = 4000(0.87)^x

Substitute x=5x = 5:

y=4000(0.87)5y = 4000(0.87)^5

Now, we calculate:

y=4000×(0.87)5y = 4000 \times (0.87)^5

y=4000×0.513y = 4000 \times 0.513

y2052y \approx 2052

So, the value of the computer equipment 5 years after it was purchased is approximately $2,052.

Would you like further details or have any questions? Here are some related questions for you:

  1. What is the rate of depreciation in this model?
  2. How much is the equipment worth after 10 years?
  3. How do exponential decay models compare to linear decay models?
  4. What does the base 0.870.87 represent in this context?
  5. How would the value change if the rate of depreciation were increased to 0.900.90?

Tip: In exponential decay, the base of the exponent is always less than 1, showing how the value decreases over time.

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Math Problem Analysis

Mathematical Concepts

Exponential Decay
Algebra
Exponential Functions

Formulas

y = 4000(0.87)^x

Theorems

Exponential Decay Model

Suitable Grade Level

Grades 8-10