- Analyze each scenario by comparing the original amount to the new amount.
- A percent increase occurs if and only if the new amount is greater than the original amount.
- Compare the values: \(118 < 978\), \(678 > 574\), and \(1,045 < 1,254\).
- Conclude that only the second scenario shows an increase, resulting in \(\boxed{\text{Original amount} = 574, \text{New amount} = 678, \text{Percent change} = 18\%}\).
Explanation
- Problem Analysis and Defining Percent Increase
To identify which scenario represents a percent increase, we analyze the relationship between the original amount and the new amount for each provided case. A percent increase occurs when the final (new) amount is greater than the initial (original) amount. Conversely, if the new amount is less than the original, it represents a percent decrease. We will examine each of the three scenarios individually by comparing the two values given.
- Evaluating the Scenarios
In the first scenario, the original amount is 978 and the new amount is 118. Since \(118 < 978\), the value has decreased. Thus, this does not represent a percent increase. In the second scenario, the original amount is 574 and the new amount is 678. Since \(678 > 574\), the value has increased. This scenario represents a percent increase. Finally, in the third scenario, the original amount is 1,254 and the new amount is 1,045. Since \(1,045 < 1,254\), the value has decreased, which does not represent a percent increase.
- Conclusion
After evaluating each of the three scenarios based on the condition that the new amount must exceed the original amount, it is clear that only the second scenario satisfies this condition. Therefore, the second option is the only one representing a percent increase. \(\boxed{\text{Original amount} = 574, \text{New amount} = 678, \text{Percent change} = 18\%}\).
Examples
Understanding percent increases is essential for tracking growth in everyday scenarios, such as investment returns, changes in business revenue, or even tracking the growth of a plant over time. For example, if you deposit \(\$500\) into a savings account and it grows to \(\$550\) after a year, you can quickly determine that the account saw a percent increase of 10% because the ending balance is higher than the starting balance. Mastering this concept helps you analyze financial data, evaluate performance, and make informed decisions based on whether a value is trending upward or downward.