QUESTION $4$

The perceived decrease in air temperature felt by the body on exposed skin due to the flow of air is being modeled through wind$-$chill index $(W)$ by the following function.

$W=13\mathrm{.}12+0\mathrm{.}6215T-11\mathrm{.}37v^{0\mathrm{.}16}+0\mathrm{.}3965T{v}^{0\mathrm{.}16}$

If temperature $(T)=-15C$ and wind speed $(v)=30k\frac{m}{h},$ analyze the expected apparent temperature to be dropped if

$($a$)$ the actual temperature decreases by $1C$

$($b$)$ the wind speed increases by $1k\frac{m}{h}$

$(25$ marks$)$