The wind-chill index (in degrees C) is modeled by the function W = 13.12 + 0.621

Question

The wind-chill index (in degrees C) is modeled by the function W = 13.12 + 0.62157 - 11.37v^0.16 + 0.39657v^0.16 where 7 is the air-temperature (degree C) and v is the wind speed (km/h). When 7 = 6degreeC and v = 18 km/h, at what rate is windchill changing as air-temperature increases? (Round your answers to two decimal places.) degree C of windchill per C of air-temperature When 7 = 6 degree C and v = 18 km/h, , at what rate is windchill changing as wind-speed increases? (Round your answers to two decimal places.) degree C of windchill per km/hr of wind-speed

Explanation / Answer

dW/dt = 0.6215 + 0.3965v^0.16

dW/dv = -11.37.(+0.16).v^-0.84 + 0.3965.T.(+0.16).v^-0.84

= -1.82.v^(-0.84) + 0.063.T.v^(-0.84)

Now,

At T = 6 and v = 18

dW/dt = 1.25

dW/dv = 0.1269

So when at that situation the temperature drops 1 degree, W drops by 1.25

So when at that situation the wind speed increases by 1 km/h, W drops by 0.1269

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