Question

If the temperature decreases by 2 degrees per 1000 feet of gained altitude and if the temperature at sea level is 25 degrees what would the temperature at 35,000 feet be?

Answer 1

Answer:

-45 degrees

Step-by-step explanation:

35,000 ÷ 1000 = 35. This means 1000 feet will be gained 35 times. 35 × 2 = 70. This means 70 degrees will be lost as altitude increases. 25 - 70 = -45. You start with 25, so you must subtract the temperature that is lost.

Answer 2

This question is solved using a linear model, as the decay of the temperature for each 1000 feet is the same.

Doing this, we get that the temperature at 35,000 feet of altitude will be of -45 degrees.

Linear model:

A linear model, for the temperature T in function of the height h, has the following format:

$T(h) = T(0) - ah$

In which T(0) is the temperature at sea level, and a is how much it changes for each additional feet.

Temperature at sea level is 25 degrees

This means that $T(0) = 25$, so:

$T(h) = 25 - ah$

Decreases by 2 degrees per 1000 feet of gained altitude:

This means that:

$a = -\frac{2}{1000} = 0.002$

Thus

$T(h) = 25 - 0.002h$

What would the temperature at 35,000 feet be?

This is T(35000). So

$T(35000) = 25 - 0.002(35000) = -45$

Thus, the temperature at 35,000 feet would be of -45 degrees.

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