- Define the initial temperature as \(V_{initial} = 120\) and the final temperature as \(V_{final} = 100\).
- Calculate the absolute change: \(\Delta V = 100 - 120 = -20\).
- Find the fractional change: \(\frac{-20}{120} = -\frac{1}{6}\).
- Convert to a percentage: \(-\frac{1}{6} \times 100\% \approx -16.67\%\), which rounds to approximately \(17\%\).
- The correct option is (c), \(\boxed{17\%}\).
Explanation
- Analyzing the Problem and Defining the Formula
To find the percent change in temperature when it decreases from an initial value of \(120\) degrees to a final value of \(100\) degrees, we first identify the initial and final quantities:
Initial value, \(V_{initial} = 120\).
Final value, \(V_{final} = 100\).
The formula for calculating the percent change is:
\[\text{Percent Change} = \left( \frac{V_{final} - V_{initial}}{V_{initial}} \right) \times 100\%\]
This formula allows us to determine the relative decrease of the value compared to its original starting point.
- Calculating the Percent Change
We calculate the absolute change in temperature:
\[\Delta V = V_{final} - V_{initial} = 100 - 120 = -20\]
The negative sign indicates a decrease in temperature.
Next, we divide this change by the initial value:
\[\frac{\Delta V}{V_{initial}} = \frac{-20}{120} = -\frac{1}{6}\]
To convert this fraction to a percentage, we multiply by 100:
\[-\frac{1}{6} \times 100\% \approx -16.67\%\]
The magnitude of this percent decrease is approximately \(16.67\%\). Rounding to the nearest whole percentage point, we find the decrease is approximately \(17\%\). Comparing this to our options, it matches option (c).
Examples
Understanding percent change is essential in many everyday situations, such as managing your finances. For instance, if a store has a sale and lowers the price of an item from \(\$120\) to \(\$100\), knowing the percent change helps you evaluate the value of the discount. By calculating the change as a percentage of the original price, you can easily compare different discounts and make informed purchasing decisions. This simple mathematical tool is used by consumers, businesses, and scientists alike to analyze trends and changes in values over time.