Answer to Question #304172 in Calculus for itz_perfect

Question

A measure of how hot weather feels to an average person is the Apparent Temperature Index.

A model for this index is:

A = 0.885t − 22.4h + 1.20th − 0.544,

where A is the apparent temperature in degrees Celsius, t is the air temperature, and h is the

relative humidity in decimal form.

a) Find ∂A/∂t and ∂A/∂h when t = 300 and h = 0.80.

b) Which has a greater effect on A, air temperature or humidity? Explain.

Answer 1

a)

$$\partial A/\partial t=0.885+1.20h$$

$$\partial A/\partial h=-22.4+1.20t$$

$t=300, h=0.80$

$$\partial A/\partial t=0.885+1.20(0.80)=1.845$$

$$\partial A/\partial h=-22.4+1.20(300)=337.6$$

b)

Since $|\partial A/\partial h|>|\partial A/\partial t|,$ then relative humidity has a a greater effect on A, than air temperature.