Question

The temperature in a building rose from \(19.0^{\circ} \mathrm{C}\) to \(21.0^{\circ} \mathrm{C}\) during the day. Find the percent change in temperature.

Short answer

The percent change in temperature is 10.53%.

Step-by-step solution

Calculate the Change in Temperature

Determine the amount of change in temperature by subtracting the initial temperature from the final temperature. For this problem, subtract the starting temperature of 19.0 degrees Celsius from the ending temperature of 21.0 degrees Celsius.

Calculate the Percentage Change

Use the formula for percent change, which is: Percent Change = (Change in Value / Original Value) * 100%. In this case, divide the change in temperature by the original temperature and then multiply by 100%.

Solve

Substitute the values into the percent change formula and simplify to find the percent change in temperature.

Key concepts

Understanding Temperature Change

Temperature change plays a critical role in countless real-world scenarios, from the behavior of materials to the comfort levels in our living spaces. When it comes to calculating temperature change, it's essentially about capturing how much the temperature has increased or decreased over a period of time.

In our example, the temperature change was from an initial value of 19.0 degrees Celsius (the original temperature) to a final value of 21.0 degrees Celsius (the new temperature). The change in temperature is simply the difference between these two values. Understanding this change is useful not only in daily activities, such as adjusting heating or cooling systems, but also in scientific research where temperature regulation is critical.

It is important to accurately measure the initial and final temperatures using a consistent scale (Celsius, Fahrenheit, etc.) to ensure the calculations are correct. Temperature change is not only about the change in numerical value, but also about the resulting effects on the environment or a system.

Mathematical Problem-Solving Strategies

Problem-solving in mathematics involves a systematic approach to arriving at a solution. In the context of calculating percent change in temperature, these are the steps students should ideally follow:

• Identify: Determine what you are trying to find; in this case, the percent change in temperature.
• Set up: Use the appropriate formula or method; the percent change formula is the tool needed for this scenario.
• Calculate: Perform the necessary computations; subtract the original temperature from the new temperature to find the change.
• Solve: Substitute the numeric values into the formula and solve for the answer.
• Interpret: Understand what the resulting percentage means in the given context.

These strategies encourage a structured method of tackling the exercise, reducing errors and aiding comprehension. For instance, steps like identifying the problem help zero in on the mathematical tools needed, while interpretation assists in understanding the real-world implications of the mathematical result.

Applying the Percent Change Formula

The percent change formula is an essential mathematical tool used to determine the relative change between an original value and a new value, expressed as a percentage. The formula is written as:
\[\begin{equation} \text{Percent Change} = \left(\frac{\text{Change in Value}}{\text{Original Value}}\right) \times 100\% \end{equation}\]
Applying this formula involves a few straightforward steps. First, find the absolute change by subtracting the original value from the new value. Then, divide this change by the original value. Finally, multiply the result by 100 to convert it to a percentage.

For example, with the temperature in our exercise initially at 19.0 degrees Celsius and rising to 21.0 degrees Celsius, the change is 2.0 degrees. When we divide this by the original 19.0 degrees and multiply by 100, we get the percent change. This calculation can help us understand not just temperature changes, but also changes in prices, populations, and other data over time. It is crucial for students to grasp not only how to perform these calculations, but also why they matter and how they can be used to make informed decisions based on analytical findings.