Question

complete the sentences. the bacterial populations growth rate between minutes 90 and 120 was dropdown its growth rate between minutes 60 and 90. its growth rate between minutes 120 and 150 was dropdown its growth rate between minutes 90 and 120. its growth rate between minutes 150 and 180 was dropdown its growth rate between minutes 120 and 150.

Explanation:

Step1: Understand Growth Rate from Graph

Growth rate is the slope of the line segment between two points (time, population). A steeper slope means a higher growth rate.

Step2: Analyze 90 - 120 vs 60 - 90

• Let's assume population at 90: \( P_{90} \), 120: \( P_{120} \), 60: \( P_{60} \), 90: \( P_{90} \).
• Slope (growth rate) between 90 - 120: \( \frac{P_{120}-P_{90}}{120 - 90}=\frac{P_{120}-P_{90}}{30} \)
• Slope between 60 - 90: \( \frac{P_{90}-P_{60}}{90 - 60}=\frac{P_{90}-P_{60}}{30} \)
• From the graph, the curve is getting steeper, so \( P_{120}-P_{90} > P_{90}-P_{60} \). Thus, growth rate 90 - 120 is greater than 60 - 90.

Step3: Analyze 120 - 150 vs 90 - 120

• Slope 120 - 150: \( \frac{P_{150}-P_{120}}{150 - 120}=\frac{P_{150}-P_{120}}{30} \)
• Slope 90 - 120: \( \frac{P_{120}-P_{90}}{30} \)
• The curve is steeper, so \( P_{150}-P_{120} > P_{120}-P_{90} \). Growth rate 120 - 150 is greater than 90 - 120.

Step4: Analyze 150 - 180 vs 120 - 150

• Slope 150 - 180: \( \frac{P_{180}-P_{150}}{180 - 150}=\frac{P_{180}-P_{150}}{30} \)
• Slope 120 - 150: \( \frac{P_{150}-P_{120}}{30} \)
• The curve is steeper, so \( P_{180}-P_{150} > P_{150}-P_{120} \). Growth rate 150 - 180 is greater than 120 - 150.

Answer:

1. The bacterial population’s growth rate between minutes 90 and 120 was greater than its growth rate between minutes 60 and 90.
2. Its growth rate between minutes 120 and 150 was greater than its growth rate between minutes 90 and 120.
3. Its growth rate between minutes 150 and 180 was greater than its growth rate between minutes 120 and 150.