A café buys an espresso machine for $2,800 The machine depreciates by 18% annually. How long will it take for the value of the machine to drop below $1,000 ? The equation modeling this depreciation is y=2800⁢(0.82)^x

Set the value equal to $1,000 to find when it reaches the threshold: 2800(0.82)^x = 1000. Solving gives x = ln(1000/2800) ÷ ln(0.82) ≈ 5.19 years. The value drops below $1,000 just after this point, so the matching choice is 5.19 years.

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