Question: 23. The Military The graph below shows the numbers of active-duty U.S. military personnel, in thousands, in 1990 and in 2009. Which branch of the military had the greatest percent decrease in personnel from 1990 to 2009? What was the percent decrease for this branch of the service?\n\nNumber of Active-Duty U.S. Military Personnel\nPersonnel (in thousands)\n1990\n2009\nArmy\nNavy\nAir Force\nMarines\n732\n553\n579\n330\n535\n335\n196\n204
1. **State the problem:** We need to find which branch of the U.S. military had the greatest percent decrease in active-duty personnel from 1990 to 2009, and calculate that percent decrease.\n\n2. **Data given:**\n- Army: 1990 = $732$, 2009 = $535$\n- Navy: 1990 = $553$, 2009 = $335$\n- Air Force: 1990 = $579$, 2009 = $196$\n- Marines: 1990 = $330$, 2009 = $204$\n\n3. **Formula for percent decrease:**\n$$\text{Percent Decrease} = \frac{\text{Original} - \text{New}}{\text{Original}} \times 100$$\nThis formula calculates how much the number decreased relative to the original number, expressed as a percentage.\n\n4. **Calculate percent decrease for each branch:**\n\n- Army:\n$$\frac{732 - 535}{732} \times 100 = \frac{197}{732} \times 100$$\nIntermediate step with cancellation:\n$$\frac{\cancel{197}}{\cancel{732}} \times 100 \approx 26.91\%$$\n\n- Navy:\n$$\frac{553 - 335}{553} \times 100 = \frac{218}{553} \times 100$$\nIntermediate step with cancellation:\n$$\frac{\cancel{218}}{\cancel{553}} \times 100 \approx 39.42\%$$\n\n- Air Force:\n$$\frac{579 - 196}{579} \times 100 = \frac{383}{579} \times 100$$\nIntermediate step with cancellation:\n$$\frac{\cancel{383}}{\cancel{579}} \times 100 \approx 66.15\%$$\n\n- Marines:\n$$\frac{330 - 204}{330} \times 100 = \frac{126}{330} \times 100$$\nIntermediate step with cancellation:\n$$\frac{\cancel{126}}{\cancel{330}} \times 100 \approx 38.18\%$$\n\n5. **Compare the percent decreases:**\n- Army: $26.91\%$\n- Navy: $39.42\%$\n- Air Force: $66.15\%$\n- Marines: $38.18\%$\n\n6. **Conclusion:** The Air Force had the greatest percent decrease in personnel from 1990 to 2009, with a decrease of approximately $66.15\%$.