Question

The wind-chill index is modeled by the function below where T is the temperature (°C) and v is the wind speed (km/h).
W = 13.12 + 0.6215T - 11.37v0.16 + 0.3965Tv0.16
When T = 13°C and v = 34 km/h, by how much would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Enter your answer to 1 decimal place.)
____ °C

What if the wind speed increases by 1 km/h?(Enter your answer to 2 decimal places.)
_____ °C

Answer 1

When T= 13°C and v = 34 km/h
W = 13.12 + 0.6215(13) - 11.37(34)^0.16 + 0.3965(13)(34)^0.16 = 13.12 + 8.0795 - 11.37(1.7581) + 5.1545(1.7581) = 21.1995 - 19.9893 + 9.0620 = 10.27°C.

If T decrease by 1°C (T = 12°C), then
W = 13.12 + 0.6215(12) - 11.37(34)^0.16 + 0.3965(12)(34)^0.16 = 8.95°C
Therefore, W decreased by 10.27°C - 8.95°C = 1.3°C

If v increases by 1 km/h (v = 35 km/h), then
W = 13.12 + 0.6215(13) - 11.37(35)^0.16 + 0.3965(13)(35)^0.16 = 10.22°C
Therefore, W decreaseb by 10.27°C - 10.22°C = 0.05°C