Question

the bacterial population did not have a constant growth rate, so it did not exhibit linear growth.
the bacterial population exhibited exponential growth. when a population grows exponentially, its growth rate increases as the size of the population increases. on a graph, exponential growth is modeled by a j - shaped curve.
bacterial population
complete the sentences.
the bacterial populations growth rate between minutes 90 and 120 was
its growth rate between minutes 60 and 90.
its growth rate between minutes 120 and 150 was
its growth rate between minutes 90 and 120.
its growth rate between minutes 150 and 180 was
its growth rate

Explanation:

Step1: Understand Exponential Growth

Exponential growth means the growth rate increases as the population size increases. The graph's slope (which represents growth rate) should become steeper over time.

Step2: Analyze 60 - 90 vs 90 - 120

• Find population at 60, 90, 120. Assume at 60: \( P_{60} \), 90: \( P_{90} \), 120: \( P_{120} \).
• Growth rate 60 - 90: \( \frac{P_{90}-P_{60}}{90 - 60} \)
• Growth rate 90 - 120: \( \frac{P_{120}-P_{90}}{120 - 90} \)
• From the graph, the slope (growth rate) between 90 - 120 is steeper than 60 - 90, so it's greater.

Step3: Analyze 90 - 120 vs 120 - 150

• Similarly, growth rate 120 - 150: \( \frac{P_{150}-P_{120}}{150 - 120} \)
• The slope between 120 - 150 is steeper than 90 - 120, so growth rate is greater.

Step4: Analyze 150 - 180 vs 120 - 150

• Growth rate 150 - 180: \( \frac{P_{180}-P_{150}}{180 - 150} \)
• The slope between 150 - 180 is steeper than 120 - 150, so growth rate is greater.

Answer:

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