Question

The wind-chill index is modeled by the function W = 13.12 + 0.6215T − 11.37v0.16 + 0.3965Tv0.16 where T is the temperature (°C) and v is the wind speed (km/h). When T = 12°C and v = 18 km/h, by how much would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Round your answers to two decimal places.)

Answer 1

Answer:

Δw=1.25°C

Explanation:

Given that

$w=13.12 +0.6215 T-11.37 v^{0.16}+0.3965 T v^{0.16}$

Given that T= 12°C and v=19 km/h

Now to find the drop in the apparent temperature w

$\dfrac{dw}{dT}=0.6215 +0.3965v^{0.16}$

So

$\dfrac{\Delta w}{\Delta T}= 0.6215 +0.3965 v^{0.16}$

Now by putting the values v=19 km/hr and ΔT=1

$\dfrac{\Delta w}{1}=0.6215 +0.3965\times 18^{0.16}$

Δw=1.25°C

So we can say that when temperature is decrease by 1°C then apparent temperature will decrease by 1.25°C at given velocity.

Answer 2

This question involves the concepts of derivative, apparent temperature, actual temperature, and wind speed.

The drop in apparent temperature will be "1.25°C".

The apparent temperature (W) is given in terms of actual temperature (T) and wind speed (v) is given by the following function:

$W = 13.12 + 0.6215\ T-11.37\ v^{0.16}+0.3965\ Tv^{0.16}$

Taking the derivative with respect to actual temperature, we get:

$\frac{dW}{dT}=0.6215+0.3965\ v^{0.16}$

where,

dW = drop in apparent temperatures = ?

dT = drop in actual temperature = - 1°C

v = wind speed = 18 km/h

Therefore,

$dW=(-1)(0.6215-0.3965(18)^{0.16})$

dW = - 1.25°C

Learn more about derivatives here:

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