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.)

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:

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

where,

dW = drop in apparent temperatures = ?

dT = drop in actual temperature = - 1°C

v = wind speed = 18 km/h

Therefore,

dW = - 1.25°C

Learn more about derivatives here:

link

Δw=1.25°C

Explanation:

Given that

Given that T= 12°C and v=19 km/h

Now to find the drop in the apparent temperature w

So

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

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.