- List all daily balances provided in the table: \(-\$61.52, \$912.52, \$225.78, -\$228.82, -\$168.55, \$27.58\).
- Identify the negative values as the potential candidates for the minimum balance: \(-\$61.52, -\$228.82, -\$168.55\).
- Compare the absolute values of these candidates to find the most negative value, which is \(-\$228.82\).
- Associate this value with the date 3-05-2013 to conclude that it is the lowest balance.
- Final answer: \(\boxed{3-05-2013}\).
Explanation
- Analysis of the Bank Account Balances
To determine which date had the lowest account balance, we first list all the given values from the table:
- 2-20-2013: \(-\$61.52\)
- 2-25-2013: \(\$912.52\)
- 2-28-2013: \(\$225.78\)
- 3-05-2013: \(-\$228.82\)
- 3-06-2013: \(-\$168.55\)
- 3-08-2013: \(\$27.58\)
The objective is to find the minimum value among these balances. Since some values are negative and some are positive, the smallest value must be among the negative balances.
- Comparing the Negative Balances
We identify the negative balances from the provided data:
- \(-\$61.52\)
- \(-\$228.82\)
- \(-\$168.55\)
To compare these, we consider their positions on the number line. A negative number with a larger absolute value is smaller than a negative number with a smaller absolute value.
- \(\vert -228.82 \vert = 228.82\)
- \(\vert -168.55 \vert = 168.55\)
- \(\vert -61.52 \vert = 61.52\)
Since \(228.82 > 168.55 > 61.52\), the negative number \(-228.82\) is the furthest to the left on the number line, making it the smallest value. Therefore, the balance of \(-\$228.82\) on 3-05-2013 is the lowest account balance.
- Final Conclusion
By comparing all the provided balances, we determined that \(-228.82\) is the lowest numerical value in the set. This balance corresponds to the date 3-05-2013. Thus, the account balance was the lowest on 3-05-2013. The final answer is \(\boxed{3-05-2013}\).
Examples
Managing personal finances often involves tracking daily account balances to ensure you do not drop below a certain threshold. By comparing these balances over time, one can identify periods of high expenditure or financial strain. For example, if you are monitoring your savings, knowing which date represents your lowest balance helps you identify specific events or purchases that impacted your financial health the most. Mathematical comparison allows you to make informed decisions about your budget and spending habits.