To find: The percent of moisture in the central Sierra Nevada (a m

mattgondek4

mattgondek4

Answered question

2021-08-14

To find:
The percent of moisture in the central Sierra Nevada (a mountain range in California), to the nearest tenth that falls as snow at each altitude (a) 3000 ft (b) 4000 ft (c) 7000 ft using the model f(x)=86.3Inx680, where x is altitude in feet and f(x) is the percent of moisture that falls as snow.

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-08-15Added 99 answers

Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is f(x)=86.3Inx680
where x is altitude in feet and f(x) is the percent of moisture that falls as snow.
So, in order to get the percent of moisture f(x), replace x in the given model with the values of altitudes.
a) Let x=3000ft
f(x)=86.3Inx680
Replace x with 3000,f(3000)=86.3(In3000)680
Using calculator, f(3000)86.3×8.00636680
Multiplying, f(3000)690.9495680
Subtracting, f(3000)10.9495
Rounded to nearest tenth, f(3000)10.95
Based on this model, 10.95% of moisture falls as snow.
b) Lex x=4000ft
f(x)=86.3Inx680
Replace x with 3000,f(4000)=86.3(In4000)680
Using calculator, f(4000)86.3×8.294049680
Multiplying, f(4000)717.776483680
Subtracting, f(4000)35.7764
Rounded to nearest tenth, f(4000)35.78
Based on this model, 35.78% of moisture falls as snow.
c) Let x=7000ft
f(x)=86.3Inx680
Replace x with 7000,f(7000)=86.3(In7000)680
Using calculator, f(7000)86.3×8.853665680
Multiplying, f(7000)764.071326680
Subtracting, f(7000)84.07132
Rounded to nearest tenth, f(7000)84.07
Based on this model, 84.07% of moisture falls as snow.
Final statement:
Based on this model, 10.95% of moisture falls as snow at 300 ft, 35.78% of moisture falls as snow at 4000 ft and 84.07% of moisture falls as snow at 7000 ft.

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