Question

the bacterial population undergoes 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

graph of bacterial population growth with time elapsed (minutes) on x - axis (30, 60, 90, 120, 150, 180) and population size on y - axis

complete the sentences.

the bacterial population’s 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 between minutes 120 and 150.

Explanation:

Step1: Understand Growth Rate on 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

• At 60 minutes, population (let's estimate from graph) ≈ 6. At 90 minutes, ≈ 12. Slope (60 - 90): $\frac{12 - 6}{90 - 60} = \frac{6}{30} = 0.2$.
• At 90 minutes, ≈ 12. At 120 minutes, ≈ 30. Slope (90 - 120): $\frac{30 - 12}{120 - 90} = \frac{18}{30} = 0.6$.

0.6 > 0.2, so growth rate 90 - 120 is greater than 60 - 90.

Step3: Analyze 120 - 150 vs 90 - 120

• At 120 minutes, ≈ 30. At 150 minutes, ≈ 60. Slope (120 - 150): $\frac{60 - 30}{150 - 120} = \frac{30}{30} = 1$.

1 > 0.6, so growth rate 120 - 150 is greater than 90 - 120.

Step4: Analyze 150 - 180 vs 120 - 150

• At 150 minutes, ≈ 60. At 180 minutes, ≈ 120. Slope (150 - 180): $\frac{120 - 60}{180 - 150} = \frac{60}{30} = 2$.

2 > 1, so growth rate 150 - 180 is greater than 120 - 150.

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.