Question

suppose there is a 1.2°F drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 56.9°F, what will be the temperature when the plane reaches an altitude of 8,000 ft?

Answer 1

We have a linear model, that relates temperature with altitude.

The first senctence gives us a clue about tha rate of change (the slope) of temperature in function of the altitude.

We can write the slope, in °F/1000 ft, as:

$m=-1.2$

The temperature on the ground, where h=0, is 56.9 °F, so we can write the equation of the line as:

$T(h)=-1.2h+56.9$

When the altitude is 8,000 ft, h=8 and T is:

$T(8)=-1.2\cdot8+56.9=-9.6+56.9=47.3$

The temperature at 8,000 ft will be 47.3 °F.