In the central Sierra Nevada..

Question

In the central Sierra Nevada of California, the percent of moisture p that falls as snow rather than rain is approximated reasonably well by the following function, where x is the altitude in feet:

 

p(x)= 86.3 * ln(x) - 680

 

a) What percent of the moisture at 4000 feet falls as snow?

 

b) at what altitude does approximately 65% of moisture fall as snow? (Hint: let p(x)= 65, not 0.65)

Answer 1

p(x)= 86.3 * ln(x) - 680

 

a) What percent of the moisture at 4000 feet falls as snow?

 

p(4000) = 86.3 * ln(4000) - 680

p(4000) = 35.77%

 

b) At what altitude does approximately 65% of moisture fall as snow?

 

65% = 86.3 * ln(x) - 680

 

Add 680 to both sides:

 

745 = 86.3 * ln(x)

 

Divide both sides by 86.3:

 

8.63 = ln(x)

e^8.63 = x

 

5597.04 feet = x