In the Smoky Mountains of Tennessee, the percent of moisture that falls as snow rather than rain is approximated by \( \mathrm{P}=10.0 \) In \( \mathrm{h}-80 \), where \( P \) is the percent of snow moisture at an altitude h in feet. Find the percent of moisture that falls as snow at an altitude of \( 4,000 \mathrm{ft} \). Round to the nearest percent. A. \( 3 \% \) B. \( 4 \% \) C. \( 12 \% \) D. \( 11 \% \)

To solve for the percent of moisture that falls as snow at an altitude of \( 4,000 \) feet using the provided formula \( P = 10.0 \ln(h) - 80 \), we substitute \( h = 4000 \): 1. Calculate \( \ln(4000) \): \[ \ln(4000) \approx 8.294 \] 2. Substitute this back into the equation: \[ P = 10.0 \cdot 8.294 - 80 = 82.94 - 80 = 2.94 \] 3. Rounding \( 2.94 \) to the nearest percent gives \( 3\% \). So the answer is \( A. \) \( 3\% \). The percent of moisture that falls as snow decreases with altitude due to temperature changes and atmospheric pressure variations, which affect precipitation types. So, the higher we ascend, the more we might expect rain instead of snow depending on the local climate conditions. In the real world, this knowledge is valuable for activities like winter sports, agriculture, and even construction planning, where understanding snowfall patterns can significantly impact safety and operational efficiency. Knowing how altitude affects precipitation can lead to better resource management in snow-prone regions.