Question

Solve each application. In the central Sierra Nevada (a mountain range in California), the percent of moisture that falls as snow rather than rain is approximated reasonably well by $$f(x)=86.3 \ln x-680,$$ where $x$ is the altitude in feet and $f(x)$ is the percent of snow. Find the percent of moisture that falls as snow at each altitude. (a) $3000 \mathrm{ft}$ (b) $4000 \mathrm{ft}$ (c) $7000 \mathrm{ft}$

Name: Problem 77, Chapter 4: Precalculus
Uploaded: 2021-03-11T06:56:50-08:00
Duration: 5 min
Channel: Anas Venkitta
Description: Solve each application. In the central Sierra Nevada (a mountain range in California), the percent of moisture that falls as snow rather than rain is approximated reasonably well by f(x)=86.3 lnx-680, where x is the altitude in feet and f(x) is the percent of snow. Find the percent of moisture that falls as snow at each altitude. (a) 3000 ft (b) 4000 ft (c) 7000 ft

   Solve each application.
In the central Sierra Nevada (a mountain range in California), the percent of moisture that falls as snow rather than rain is approximated reasonably well by $$f(x)=86.3 \ln x-680,$$ where $x$ is the altitude in feet and $f(x)$ is the percent of snow. Find the percent of moisture that falls as snow at each altitude.
(a) $3000 \mathrm{ft}$
(b) $4000 \mathrm{ft}$ 
(c) $7000 \mathrm{ft}$

Precalculus

Margaret L. Lial,… 4th Edition

Chapter 4, Problem 77

Instant Answer

Solved by Expert Anas Venkitta

03/11/2021

Step 1

3 \ln x-680$, where $x$ is the altitude in feet and $f(x)$ is the percent of snow. We are asked to find the percent of moisture that falls as snow at altitudes of 3000 ft, 4000 ft, and 7000 ft. Show more…

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Solve each application. In the central Sierra Nevada (a mountain range in California), the percent of moisture that falls as snow rather than rain is approximated reasonably well by $$f(x)=86.3 \ln x-680,$$ where $x$ is the altitude in feet and $f(x)$ is the percent of snow. Find the percent of moisture that falls as snow at each altitude. (a) $3000 \mathrm{ft}$ (b) $4000 \mathrm{ft}$ (c) $7000 \mathrm{ft}$

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Key Concepts

Function Modeling

This concept involves representing relationships between variables using mathematical expressions. By modeling a real-world phenomenon—like the percentage of moisture that falls as snow—as a function of another variable such as altitude, we can analyze how changes in one affect the other.

Logarithmic Function

A logarithmic function, especially the natural logarithm (ln), is used to model situations where changes occur at a rate proportional to the current value. Its properties allow it to capture phenomena with diminishing returns, as often seen in natural processes.

Domain and Interpretation in Applied Contexts

When using mathematical functions to describe real-world scenarios, it is important to consider the domain of the function (the set of valid inputs) and interpret the results in context. Here, altitude is the input, and the function’s output is interpreted as a percentage, highlighting the need for correct units and realistic ranges.

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