Practice question · Estimate

Equipment worth 80k€ depreciates continuously at $r = -10\%$ /year. Set the slider to its approximate value after 7 years (k€). Note $e^{-0.7} \approx 0.5$ .

Estimate on a scale from 0k€ (0) to 80k€ (80).

Hints

$x(7) = 80\,e^{-0.7}$ .
The rule of 70 in reverse: 10% decay halves in ~7 years.

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40 (answers within ±3 count)

Why

$80 \cdot e^{-0.7} \approx 80 \cdot 0.5 = 40$ k€. The rule of 70 works for decay too: at 10% the half-life is about 7 years, depreciation schedules are radioactive decay wearing a suit.

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Equipment worth 80k€ depreciates continuously at r=−10%r = -10\%r=−10%/year. Set the slider to its approximate value after 7 years (k€). Note e−0.7≈0.5e^{-0.7} \approx 0.5e−0.7≈0.5.

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Equipment worth 80k€ depreciates continuously at $r = -10\%$ /year. Set the slider to its approximate value after 7 years (k€). Note $e^{-0.7} \approx 0.5$ .