Pregunta
TB. DAVs (LMS) There are 1,200 fruit flies in a lab. The population decreases \( 10 \% \) per day. Compare the decrease in the population for days 1 to 3 with the decrease for days 4 to 6 . Complete the sentence. The population decreases Choose... from day 1 to day 3 than from day 4 to day 6 .
Ask by Newton Bolton. in the United States
Jan 30,2025
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The population decreases more from day 1 to day 3 than from day 4 to day 6.
Solución
The population decreases **more** from day 1 to day 3 than from day 4 to day 6.
**Explanation:**
The fruit fly population decreases by 10% each day, which means it undergoes exponential decay. Here's how the population changes:
- **Days 1 to 3:**
- **Day 1:** \( 1200 \times 0.9 = 1080 \)
- **Day 2:** \( 1080 \times 0.9 = 972 \)
- **Day 3:** \( 972 \times 0.9 = 874.8 \)
- **Total decrease:** \( 1200 - 874.8 = 325.2 \) flies
- **Days 4 to 6:**
- **Day 4:** \( 874.8 \times 0.9 = 787.32 \)
- **Day 5:** \( 787.32 \times 0.9 = 708.588 \)
- **Day 6:** \( 708.588 \times 0.9 = 637.7292 \)
- **Total decrease:** \( 874.8 - 637.7292 = 237.0708 \) flies
Comparing the two periods:
- **Days 1-3:** Decrease of approximately **325** flies
- **Days 4-6:** Decrease of approximately **237** flies
Thus, the population decreases **more** in the first three days than in the subsequent three days.
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The Deep Dive
The population decreases **more rapidly** from day 1 to day 3 than from day 4 to day 6. To illustrate this: On day 1, you start with 1,200 fruit flies. After a 10% decrease, you’re left with 1,080 flies. This trend continues, leading to a sharper decline in the initial days. By day 4, the population has shrunk significantly, meaning that while the percentage decrease remains the same, the actual number of flies lost daily becomes smaller, resulting in a slower decrease by days 4 to 6.
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