Express temperature as a function of height, using linear model?The ground temperature is 20 degrees C. The temperature of 10 degrees C is at a...

Given:

Temperature at ground level, that is when height is 0 (h0) meters

= t0 = 20 degrees centigrade

Temperature at height 1 km (h) meters

= t = 10 degrees centigrade

It is assumed that the temperature drops in proportion to increase in height.

This can be expressed in the form of equation as follows:

t = t0 - C*(h - h0)   ...   (1)

Where C is a constant.

Substituting values of t0, t h0 and h in equation (1) we get:

10 = 20 - C*(1 - 0) = 20 - C

Therefore:

C = 20 - 10 = 10

Substituting value of C, t0, and h0 in equation (1) we get:

t = 20 - 10*(h - 0) = 20 - 10h

Therefore temperature can be expressed as a function of height by the equation:

Temperature in degrees centigrade = 20 - 10*(Height in km)