Problem 109 - Intermediate Algebra

Question

The highest and lowest temperatures ever recorded in several cities are shown in the table. List the cities in order, from the smallest to the largest range in temperature extremes. $$ \begin{array}{|l|c|c|} \hline \multirow{2}{*}\text { City } & \multicolumn{2}{|c|}\begin{array}{c} \text { Extreme } \\ \text { temperatures } \end{array} \\ \hline & \text { Highest } & \text { Lowest } \\ \hline \text { Atlanta, Georgia } & 105 & -8 \\ \hline \text { Boise, Idaho } & 111 & -25 \\ \hline \text { Helena, Montana } & 105 & -42 \\ \hline \text { New York, New York } & 107 & -3 \\ \hline \text { Omaha, Nebraska } & 114 & -23 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

New York, Atlanta, Boise, Omaha, Helena (in order of increasing temperature range).

Step 1: Determine the Temperature Range for Each City

To find the temperature range for each city, subtract the lowest recorded temperature from the highest recorded temperature. 1. **Atlanta, Georgia**: \(105 - (-8) = 113\)2. **Boise, Idaho**: \(111 - (-25) = 136\)3. **Helena, Montana**: \(105 - (-42) = 147\)4. **New York, New York**: \(107 - (-3) = 110\)5. **Omaha, Nebraska**: \(114 - (-23) = 137\)

Step 2: List the Cities by Temperature Range

Now that we have calculated the range for each city, list them in ascending order based on their temperature ranges: - **New York, New York**: 110 - **Atlanta, Georgia**: 113 - **Boise, Idaho**: 136 - **Omaha, Nebraska**: 137 - **Helena, Montana**: 147

Key Concepts

Extreme Temperatures

Extreme temperatures provide an insight into how varied the climate of a place can be. They are the most outstanding hot and cold temperatures ever experienced in a location. Knowing about extreme temperatures helps in understanding the climate challenges of a city.
These values are essential for several reasons:

• Planning Infrastructure: Engineers use this data to plan for buildings and roads that can withstand these temperature extremes.
• Emergency Preparedness: Authorities need to be prepared for both heatwaves and cold snaps by understanding the range of possible temperatures.
• Climate Study: Scientists study records of extreme temperatures to understand climate patterns and changes over time.

Analyzing extremes rather than averages provides a real picture of what weather conditions a city might encounter.

City Temperature Data

City temperature data comprises the recorded highs and lows experienced in a city. This data is collected continuously and forms the foundation for climate analysis.
For anyone interested in understanding climate trends, it's essential to pay attention to this data. Here's why it's important:

• Historical Comparison: Observing temperature changes over time can show how urbanization or other factors have altered a city's climate.
• Local Climate Classification: Cities can be classified climatically based on their temperature data, helping in urban planning and development.
• Public Awareness: When the public understands their city's temperature range, it promotes awareness and readiness for weather-related challenges.

This data is often shown in tables, graphs, or maps to make it as clear and accessible as possible.

Temperature Calculations

Understanding temperature calculations is key to deducing various climate characteristics of a city. The primary calculation used here is the temperature range.
To find the temperature range, one must subtract the lowest recorded temperature from the highest. Here is the approach:

• Identify the highest and lowest temperatures recorded in a city.
• Apply the formula: \( \text{Range} = \text{Highest} - \text{Lowest} \)

For instance, in Helena, Montana, the highest temperature recorded is 105°F and the lowest is -42°F. So, the temperature range is \(105 - (-42) = 147\) degrees.
This straightforward calculation allows us to compile a list of cities based on their climate variability, from low to high ranges. It highlights how cities can differ in their susceptibility to weather extremes.