Solve the equation

Question

As dry air moves upward, it expands and in so doing cools at a rate of about 1 degree c for 100m rise, up to about 12km.

if the ground temp is 17 degrees, write a formula for the temp at height x km.

what range can be expected if a plane takes off and reaches a maximum height of 10km. Write answer in interval notation.

Answer 1

Dry air moves upward, it expands and cools at a rate of about for rise, about .

The ground temp is .

(a)

Find a formula for the temp at height .

Let is a height in meters.

is a temperature.

At ground level it is at .

Hence, it goes down for every .

At , it would be extra.

(b)

Find a plane takes off and reached a maximum height of .

Here,

A plane takes off and reached a maximum height of is

A plane takes off and reached a maximum height of is

The interval notation is .