It's winter and the powder on Vail Mountain has never been better. You decide to measure the snowfall over a three hour period to determine the amount of snow that has fallen. The first hour you record a 5% increase in snowfall, the second hour you record a 8% increase in snowfall, and the third hour you record a 11% increase in snow fall. Over the three hour period, the snow has increased to a height of 17 inches. How high was the snow on the first hour just before it started to snow? Round your answers to the nearest tenth of an inch.
Let the snow’s height before the first hour be x. The three increases are successive, so the final height is x × 1.05 × 1.08 × 1.11 = 17. Solving gives x = 17 ÷ 1.25874 ≈ 13.5 inches, so the best answer is 13.5 inches.
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