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 into the given equation:
Substitute :
Now, we calculate:
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:
- What is the rate of depreciation in this model?
- How much is the equipment worth after 10 years?
- How do exponential decay models compare to linear decay models?
- What does the base represent in this context?
- How would the value change if the rate of depreciation were increased to ?
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
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