2) 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 < 8418

where x is the altitude in feet and f(x) is the percent of moisture that falls as snow.

a) Find the domain of this function and interpret the domain in context to the problem. (Show work, interpret your domain using proper units)

Question

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MrRoyal MrRoyal · Answer 1 · 2021-04-23T04:00:52+02:00

Answer:

[tex]x = [2644,8418)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 86.3ln\ x - 680[/tex]

[tex]x < 8418[/tex]

Required

The domain of the function

The maximum value of x has been given.

So, the next step is to calculate its minimum value.

Since f(x) represents the % moisture. This value cannot go less than 0.

So, we set f(x) to 0; in order to calculate the minimum of x.

This gives:

[tex]f(x) = 0[/tex]

[tex]86.3ln\ x - 680 = 0[/tex]

Add 680 to both sides

[tex]86.3ln\ x - 680 + 680= 0 + 680[/tex]

[tex]86.3ln\ x = 680[/tex]

Divide both sides by 86.3

[tex]ln\ x = \frac{680}{86.3}[/tex]

[tex]ln\ x = 7.88[/tex]

Take exponent of both sides

[tex]e^{(ln\ x)} = e^{7.88[/tex]

[tex]x = e^{7.88[/tex]

[tex]x = 2644[/tex]

Hence, the domain is:

[tex]x = [2644,8418)[/tex]

or

[tex]2644 \le x< 8418[/tex]