Problem 84 - Algebra A Combined Function

Question

The airport in Bishop, California, is at an elevation of 4101 feet above sea level. The nearby Furnace Creek Airport in Death Valley, California, is at an elevation of 226 feet below sea level. How much higher in elevation is the Bishop Airport than the Furnace Creek Airport? (Source: National Climatic Data Center)

Step-by-Step Solution

Answer

4327 feet higher.

Step 1: Understanding Elevations

To find how much higher one location is compared to another, we first need to identify their elevations relative to a common reference point, such as sea level. Bishop Airport is 4101 feet above sea level, while Furnace Creek is 226 feet below sea level.

Step 2: Determine Combined Total Elevation Difference

Since Bishop Airport is above sea level and Furnace Creek is below, we add the elevations instead of subtracting them. We essentially need to calculate the total height change from 226 feet below to 4101 feet above sea level.

Step 3: Calculate the Total Difference

Add the 4101 feet above sea level at Bishop to the 226 feet below sea level at Furnace Creek. This is expressed as: \[ 4101 + 226 = 4327 \]

Step 4: Interpretation of Result

This calculation informs us that Bishop Airport is actually 4327 feet higher than Furnace Creek Airport.

Key Concepts

Above Sea Level

In geography, when we talk about a location's elevation as being 'above sea level,' we're describing how high that location is compared to the average surface level of the Earth's oceans. Sea level is often considered a zero-point reference for measuring elevation. It helps us understand how high or low particular places are in comparison.

For example, Bishop Airport is 4101 feet above sea level. This means that if you were to measure straight up from the ocean's average surface, Bishop Airport is 4101 feet higher than that level. Being above sea level has many implications, from the weather you might expect to the type of vegetation and wildlife that might thrive there.

• Impacts local climate
• Affects air pressure levels
• Influences potential flood threats

Understanding whether a location is above or below sea level is crucial for many scientific and engineering tasks, including construction, aviation, and climatology.

Below Sea Level

When a location is described as 'below sea level,' it lies under the average level of the ocean surface. Such locations are less common and often found in areas such as valleys or depressions within landscapes. This can have significant geographical and ecological impact.

Furnace Creek Airport is 226 feet below sea level. Imagine if you could see the ocean as a giant bathtub. Furnace Creek would be 226 feet down from the ocean's average surface at that point. Knowing the below-sea-level elevation of a place helps us understand aspects like:

• Susceptibility to flooding
• Atypical vegetation and fauna
• Unique weather patterns

Locations below sea level can pose serious construction challenges, especially involving water drainage and structure integrity.

Calculation of Height Difference

To figure out the elevation difference between two points, understanding how to handle mid-point references like sea level is vital. In our exercise, we calculated the height difference between Bishop and Furnace Creek Airports. Whether the elevations are above or below sea level affects how we perform the calculations.

The important step when calculating such a difference is knowing what to do when one point is above and the other is below sea level.

Here's how we calculated it:1. Note the first location's elevation: **4101 feet** above sea level (Bishop Airport).2. Note the second location's elevation: **226 feet** below sea level (Furnace Creek Airport).3. Since one is above and the other below, add these two numbers to find the difference.
\(4101 + 226 = 4327\)Therefore, Bishop is 4327 feet higher than Furnace Creek. This method of combining elevations—adding them when one is below sea level—is a key detail to remember when conducting similar geographical calculations.