Advanced MathHardEvaluating an exponential decay model
Advanced Math practice question
The value of a piece of equipment, in dollars, t years after it was purchased is modelled by V(t) = 800(0.75)^t.
According to the model, what is the value of the equipment, in dollars, after 2 years?
Answer: 450
Each year the value is multiplied by 0.75. After 2 years it has been multiplied by 0.75 twice: 800(0.75)² = 800(0.5625) = 450.
Common wrong answers
- If you answered 400
- You took 25% of the ORIGINAL 800 off twice (800 − 200 − 200). Exponential decay takes 25% of the current value each time, so the second drop is 25% of 600, not of 800.
- If you answered 600
- That's the value after ONE year: 800 × 0.75 = 600. The question asks for two years, so multiply by 0.75 again: 600 × 0.75 = 450.
- If you answered 337.5
- That's three years of decay, 800 × 0.75³. The question asks for 2 years.
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