   Chapter 14.1, Problem 6E

Chapter
Section
Textbook Problem

The wind-chill index W discussed in Example 2 has been modeled by the following function:W(T, v) = 13.12 + 0.6215T − 11.37v0.16 + 0.3965 Tv0.16Check to see how closely this model agrees with the values Table 1 for a few values of T and v.

To determine

To check: Whether the wind-chill index model w(T,v) agrees with the table values.

Explanation

Given:

The function is, w(T,v)=13.12+0.6215T11.37v0.16+0.3965Tv0.16 .

Calculation:

The Table 1 is as follows.

 v T 5 10 15 20 25 30 40 50 60 70 80 5 4 3 2 1 1 0 −1 −1 −2 −2 −3 0 −2 −3 −4 −5 −6 −6 −7 −8 −9 −9 −10 −5 −7 −9 −11 −12 −12 −13 −14 −15 −16 −16 −17 −10 −13 −15 −17 −18 −19 −20 −21 −22 −23 −23 −24 −15 −19 −21 −23 −24 −25 −26 −27 −29 −30 −30 −31 −20 −24 −27 −29 −30 −32 −33 −34 −35 −36 −37 −38 −25 −30 −33 −35 −37 −38 −39 −41 −42 −43 −44 −45 −30 −36 −39 −41 −43 −44 −46 −48 −49 −50 −51 −52 −35 −41 −45 −48 −49 −51 −52 −54 −56 −57 −58 −60 −40 −47 −51 −54 −56 −57 −59 −61 −63 −64 −65 −67

Obtain the value of w(5,5) .

Substitute T=5 and v=5 in the given model and obtain the value of w(5,5) .

w(5,5)=13.12+0.6215(5)11.37(5)0.16+0.3965(5)(5)0.16=13.12+3.107514.7094+2.5648=18.792314.7094=4.0829

The value is, w(5,5)=4.0829 .

From the Table 1, it can be identified that the value of w(5,5)=4 .

Then, obtain the value of w(40,5) .

Substitute T=40 and v=5 in the given model and obtain the value of w(40,5)

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