Question

this graph shows the growth of a population of bacteria over time (hours).
bacterial population
indicate the statements about the population that are supported by the graph:

• the bacterial populations growth rate between 90 and 120 was greater than the growth rate between 60 and 90.
• the population demonstrated linear growth.
• taking back 36 minutes (instead), the populations growth was positive.
• the population had a constant growth rate.

Explanation:

Step1: Analyze the graph trend

The graph shows the growth of a bacteria population over time (time in minutes on the x - axis and population on the y - axis). We observe the points plotted: as time increases, the population values are increasing, and the rate of increase seems to be accelerating (since the slope between consecutive points is getting steeper, which is characteristic of exponential growth).

Step2: Evaluate each statement

• Statement 1: "The bacterial population's growth rate between minutes 50 and 100 was greater than the growth rate between minutes 90 and 120."
• To check the growth rate, we can look at the change in population over the change in time. Let's assume the population at 50 minutes is \(P_{50}\), at 100 minutes is \(P_{100}\), at 90 minutes is \(P_{90}\), and at 120 minutes is \(P_{120}\). The growth rate between 50 - 100 is \(\frac{P_{100}-P_{50}}{100 - 50}=\frac{P_{100}-P_{50}}{50}\), and between 90 - 120 is \(\frac{P_{120}-P_{90}}{120 - 90}=\frac{P_{120}-P_{90}}{30}\). From the graph, the increase from 50 to 100 is less steep than from 90 to 120, so this statement is false.
• Statement 2: "The population demonstrated linear growth."
• Linear growth would have a constant slope (constant rate of change). But the graph shows that the population is increasing at an increasing rate (the distance between consecutive points on the y - axis is getting larger for the same change in x - axis), so it is not linear. This statement is false.
• Statement 3: "Taking back 30 minutes before, the population's growth was positive."
• Since the population is increasing over time (as we move from left to right on the x - axis, the y - axis values are increasing), even if we go back 30 minutes (move left on the x - axis), the population values are still increasing (the trend is upward). So the growth was positive. This statement is true.
• Statement 4: "The population had a constant growth rate."
• A constant growth rate would mean a linear graph (constant slope). But as we saw, the slope is increasing (exponential - like growth), so the growth rate is not constant. This statement is false.

Answer:

The statement "Taking back 30 minutes before, the population's growth was positive." is supported by the graph.