Question

8. For every 1,000 feet above sea level, the air temperature decreases by 4°F.The highest natural point in Texas is Guadalupe Peak at 8,751 feet. If thetemperature at sea level is 76°F, what is the temperature near the summit at8,000 feet? (Example 4)

Answer 1

The temperature at an altitude of 8,000 feet is 44° F

SOLUTION

Problem Statement

The question tells us that air temperature drops by 4 degrees Fahrenheit for every 1,000 feet above sea level. We are asked to calculate the temperature at 8,000 feet, close to the summit of Guadalupe Peak.

Solution

To solve this question, we simply compute the temperature changes for each 1,000 increase in height and then generalize. With the generalization, we can find the temperature at any height.

The temperature at 0 feet is 76°F (At sea level)

The temperature at 1,000 feet is 76°F - 4°F = 72° F

The temperature at 2,000 feet (2 x 1,000 feet) is 76°F - 4°F - 4°F (76°F - 2 x 4°F)

The temperature at 3,000 feet (3 x 1,000 feet) is 76°F - 4° F - 4° F - 4° F (76° F - 3 x 4° F)

And so on.

We can see a pattern developing and with this pattern, we can make a generalization about the temperature decrease for every increase in altitude.

`\begin{gathered} The\text{ temperature at }n*1,000\text{ feet is (}76^o-n*4^o)F \\ \text{where,} \\ n=A\text{ whole number starting from zero} \end{gathered}`

Thus, we can solve the question by substituting n = 8 for an altitude of 8,000 feet. This is done below:

8 x 1000 feet = 8,000 feet is:

`\begin{gathered} 76^oF-8*4^{o\text{ }}F \\ 76^oF-32^oF \\ =44^oF \end{gathered}`

Final Answer

The temperature at an altitude of 8,000 feet is 44° F