Question

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 from Graph

Growth rate is the slope of the line segment between two points on the population - time graph. The formula for slope (growth rate) between two points \((t_1, P_1)\) and \((t_2, P_2)\) is \(m=\frac{P_2 - P_1}{t_2 - t_1}\).

Step2: Analyze 60 - 90 and 90 - 120

• For 60 - 90 minutes: Let's assume the population at 60 minutes is \(P_{60}\) and at 90 minutes is \(P_{90}\). The time interval \(\Delta t_1=90 - 60 = 30\) minutes.
• For 90 - 120 minutes: The time interval \(\Delta t_2 = 120 - 90=30\) minutes. From the graph, the increase in population from 90 to 120 is more than from 60 to 90. So the growth rate (slope) between 90 - 120 is greater than between 60 - 90.

Step3: Analyze 90 - 120 and 120 - 150

• For 90 - 120 minutes: \(\Delta t = 30\) minutes.
• For 120 - 150 minutes: \(\Delta t=150 - 120 = 30\) minutes. From the graph, the increase in population from 120 to 150 is more than from 90 to 120. So the growth rate between 120 - 150 is greater than between 90 - 120.

Step4: Analyze 120 - 150 and 150 - 180

• For 120 - 150 minutes: \(\Delta t = 30\) minutes.
• For 150 - 180 minutes: \(\Delta t=180 - 150 = 30\) minutes. From the graph, the increase in population from 150 to 180 is more than from 120 to 150. So the growth rate between 150 - 180 is greater than between 120 - 150.

Answer:

The bacterial population’s growth rate between minutes 90 and 120 was \(\boldsymbol{\text{greater than}}\) its growth rate between minutes 60 and 90.

Its growth rate between minutes 120 and 150 was \(\boldsymbol{\text{greater than}}\) its growth rate between minutes 90 and 120.

Its growth rate between minutes 150 and 180 was \(\boldsymbol{\text{greater than}}\) its growth rate between minutes 120 and 150.