To find the percent of annual precipitation that falls as snow at an altitude of 5000 feet using the given function [tex]\( p(h) = 79 \ln(h) - 621 \)[/tex], we need to follow the steps below:
1. Determine the value of [tex]\( h \)[/tex]:
- Here, [tex]\( h = 5000 \)[/tex] feet.
2. Substitute [tex]\( h = 5000 \)[/tex] into the function:
- [tex]\( p(5000) = 79 \ln(5000) - 621 \)[/tex]
3. Compute the value of [tex]\( p(5000) \)[/tex]:
- After substituting 5000 feet into the function and performing the necessary operations, you find that the percent of annual precipitation that falls as snow at 5000 feet is approximately 52%.
Thus, the percent of annual precipitation that falls as snow at 5000 feet is approximately 52%. (Rounded to the nearest integer.)
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Similarly, to find the percent of annual precipitation that falls as snow at an altitude of 7000 feet using the same function:
1. Determine the value of [tex]\( h \)[/tex]:
- Here, [tex]\( h = 7000 \)[/tex] feet.
2. Substitute [tex]\( h = 7000 \)[/tex] into the function:
- [tex]\( p(7000) = 79 \ln(7000) - 621 \)[/tex]
3. Compute the value of [tex]\( p(7000) \)[/tex]:
- After substituting 7000 feet into the function and performing the necessary operations, you find that the percent of annual precipitation that falls as snow at 7000 feet is approximately 78%.
Thus, the percent of annual precipitation that falls as snow at 7000 feet is approximately 78%. (Rounded to the nearest integer.)
