Question

the bacterial population did not have a constant growth rate, so it did not exhibit linear growth. the bacterial population exhibited 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 complete the sentences. the bacterial populations 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: Recall exponential - growth property

In exponential growth, the growth rate increases as the population size increases.

Step2: Analyze time - intervals

For the time - interval 90 - 120 minutes and 60 - 90 minutes:
Let's assume the population at 60 minutes is $P_1$, at 90 minutes is $P_2$, at 120 minutes is $P_3$. The growth rate from 60 - 90 minutes is $\frac{P_2 - P_1}{90 - 60}$, and from 90 - 120 minutes is $\frac{P_3 - P_2}{120 - 90}$. Since it is exponential growth and $P_3 - P_2>P_2 - P_1$ (because of the J - shaped curve), the growth rate between 90 and 120 minutes is greater than the growth rate between 60 and 90 minutes.
For the time - interval 120 - 150 minutes and 90 - 120 minutes:
Let the population at 150 minutes be $P_4$. The growth rate from 120 - 150 minutes is $\frac{P_4 - P_3}{150 - 120}$. Since it is exponential growth and $P_4 - P_3>P_3 - P_2$, the growth rate between 120 and 150 minutes is greater than the growth rate between 90 and 120 minutes.
For the time - interval 150 - 180 minutes and 120 - 150 minutes:
Let the population at 180 minutes be $P_5$. The growth rate from 150 - 180 minutes is $\frac{P_5 - P_4}{180 - 150}$. Since it is exponential growth and $P_5 - P_4>P_4 - P_3$, the growth rate between 150 and 180 minutes is greater than the growth rate between 120 and 150 minutes.

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.