Question

imagine a population of bacteria growing in a petri dish with nutrient agar, a gel that provides food and space to grow. the dish has a lid that keeps bacteria from immigrating into or emigrating out of the dish. every 30 minutes, 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.
select all the statements about this population that are supported by the graph.
the population demonstrated linear growth.
during each 30 - minute interval, the population’s growth was positive.
the population had a constant growth rate.
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 Linear Growth

Linear growth has a constant slope (growth rate). But bacterial growth is usually exponential (doubling every 30 mins here). Wait, but let's check the graph points. Wait, the first statement: "The population demonstrated linear growth" – no, because exponential growth (doubling) would have a curve, but maybe the graph here? Wait, no, let's re - examine. Wait, the problem's graph: let's list the time and population. At 30 mins, let's say population is \( P_1 \), 60 mins \( P_2 \), 90 mins \( P_3 \), 120 mins \( P_4 \), 150 mins \( P_5 \), 180 mins \( P_6 \). If it's doubling every 30 mins, it's exponential. But maybe the graph here is mis - represented? Wait, no, the user's selected options: let's check each statement.

Step2: Positive Growth in Intervals

"During each 30 - minute interval, the population’s growth was positive." Since the population is increasing (from the graph, each subsequent point is higher), so this is true.

Step3: Constant Growth Rate

For linear growth, the growth rate (slope) is constant. But in exponential growth, the growth rate (in terms of percentage) is constant, but in absolute terms, it's increasing. Wait, but if the population doubles every 30 mins, the absolute growth (change in population) increases each interval. But maybe the graph here is linear? Wait, no, the first selected option says linear growth. Wait, maybe the graph has points that are linear? Wait, no, let's think again. The key is to check the selected statements.

Step4: Growth Rate Comparison

" The bacterial population’s growth rate between minutes 150 and 180 was greater than its growth rate between minutes 90 and 120." Growth rate is \( \frac{\Delta P}{\Delta t} \). If in 90 - 120 (30 mins), \( \Delta P_1 = P_4 - P_3 \), and 150 - 180 (30 mins), \( \Delta P_2 = P_6 - P_5 \). If the population is doubling, \( \Delta P_2> \Delta P_1 \), so growth rate (absolute) is higher, so this statement is true.

Wait, but the first statement "The population demonstrated linear growth" – if the population is doubling every 30 mins, it's exponential, not linear. So maybe there's a mistake in the selected option, but according to the user's marked options, we need to validate.

But let's go back to the problem: the task is to select all supported statements. Let's re - evaluate:

1. "The population demonstrated linear growth" – No, because exponential growth (doubling) has a non - linear (curved) graph. But maybe the graph here is drawn as linear? Wait, no, the user's selected option includes this, but it's incorrect. Wait, maybe the problem's graph is different. Wait, the original problem's graph: let's assume the points are (30, \( a \)), (60, \( 2a \)), (90, \( 4a \)), (120, \( 8a \)), (150, \( 16a \)), (180, \( 32a \)). This is exponential, so linear growth is wrong. But the user's selected option has it, which is a mistake. But maybe in the graph, the points are linear? Wait, no, the key is to check the correct statements.

But according to the user's marked options, we will proceed with the analysis of the correct statements (the ones that are actually supported):

- "During each 30 - minute interval, the population’s growth was positive." Since the population is increasing over each 30 - minute interval (each next data point is higher than the previous), this is supported.

- "The bacterial population’s growth rate between minutes 150 and 180 was greater than its growth rate between minutes 90 and 120." Growth rate is calculated as \( \text{Growth Rate}=\frac{\text{Change in Population}}{\text{Change in Time}} \). For a population that doubles every 30 minutes, the change in population ( \( \Delta P \)) in the interval 150 - 180 (30 minutes) will be larger than the change in the interval 90 - 120 (30 minutes) because the population is larger, so the absolute growth (and thus the growth rate if we consider absolute growth rate) is larger. So this statement is supported.

- "During each 30 - minute interval, the population’s growth was positive." As the population size is increasing at each 30 - minute mark, the growth (change in population) is positive in each interval.

The statement "The population had a constant growth rate" is incorrect for exponential growth (which is the case here, doubling every 30 minutes), and "The population demonstrated linear growth" is also incorrect for exponential growth. But according to the user's selected options, we will focus on the correct ones.

Answer:

The statements supported by the graph are:

• 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.