Question

every bacterium in the population reproduces asexually by dividing into two, which doubles the population size.
a petri dish containing growing colonies of bacteria
this graph shows the growth of a population of bacteria over three hours.
bacterial population
select all the statements about this population that are supported by the graph.
the population had a constant growth rate.
the population demonstrated linear growth.
during each 30 - minute interval, the population’s growth was positive.
the bacterial population’s growth rate between minutes 150 and 180 was greater than its growth rate between minutes 90 and 120.

Explanation:

Step1: Analyze Constant Growth Rate

To check constant growth rate, calculate the population change over each 30 - minute interval. Let's assume the population values at different times: at 30 minutes, let's say \(P_1\); at 60 minutes, \(P_2\); at 90 minutes, \(P_3\); at 120 minutes, \(P_4\); at 150 minutes, \(P_5\); at 180 minutes, \(P_6\). The change between 30 - 60 minutes: \(\Delta P_1=P_2 - P_1\), 60 - 90 minutes: \(\Delta P_2 = P_3 - P_2\), 90 - 120 minutes: \(\Delta P_3=P_4 - P_3\), 120 - 150 minutes: \(\Delta P_4 = P_5 - P_4\), 150 - 180 minutes: \(\Delta P_5=P_6 - P_5\). From the graph, we can see that the increase in population over each 30 - minute interval is not the same. For example, the growth from 150 to 180 minutes is larger than from 90 to 120 minutes. So the growth rate is not constant. So the statement "The population had a constant growth rate" is false.

Step2: Analyze Linear Growth

Linear growth implies a constant slope (constant rate of change) in the graph of population vs. time. Since we saw that the rate of change (growth rate) is not constant (the change in population over equal time intervals is not the same), the population does not demonstrate linear growth. So the statement "The population demonstrated linear growth" is false.

Step3: Analyze Positive Growth in 30 - minute Intervals

For each 30 - minute interval (30 - 60, 60 - 90, 90 - 120, 120 - 150, 150 - 180), we check if the population at the end of the interval is greater than at the start. From the graph, we can see that as time increases (moving from left to right on the x - axis), the population values (y - axis) are increasing. So during each 30 - minute interval, the population's growth was positive.

Step4: Analyze Growth Rate between 150 - 180 and 90 - 120

Growth rate \(r=\frac{\Delta P}{\Delta t}\), where \(\Delta t = 30\) minutes for both intervals. Let's find \(\Delta P\) for 90 - 120 minutes: let the population at 90 minutes be \(P_{90}\) and at 120 minutes be \(P_{120}\), \(\Delta P_{90 - 120}=P_{120}-P_{90}\). For 150 - 180 minutes: \(\Delta P_{150 - 180}=P_{180}-P_{150}\). From the graph, \(P_{180}-P_{150}>P_{120}-P_{90}\), so \(\frac{\Delta P_{150 - 180}}{30}>\frac{\Delta P_{90 - 120}}{30}\), meaning the growth rate between 150 and 180 minutes is greater than between 90 and 120 minutes.

Step5: Evaluate Each Statement

• "The population had a constant growth rate": False (as growth rate is not constant)
• "The population demonstrated linear growth": False (linear growth needs constant rate)
• "During each 30 - minute interval, the population’s growth was positive": True (population increases in each 30 - min interval)
• "The bacterial population’s growth rate between minutes 150 and 180 was greater than its growth rate between minutes 90 and 120": True (since \(\frac{\Delta P_{150 - 180}}{30}>\frac{\Delta P_{90 - 120}}{30}\))

Answer:

• During each 30 - minute interval, the population’s growth was positive.
• The bacterial population’s growth rate between minutes 150 and 180 was greater than its growth rate between minutes 90 and 120.