Question

bacterial population
select all the statements about this population that are supported by the graph.
the population grew relatively slowly for the first 12 hours.
the population grew relatively quickly between hours 14 and 18.
the population size did not change much after hour 19.
the population grew exponentially for all 24 hours.

Explanation:

Step1: Analyze first 12 hours

From \( t = 0 \) to \( t = 12 \) hours, the population (y - value) is nearly 0, so growth is slow. This supports "The population grew relatively slowly for the first 12 hours."

Step2: Analyze hours 14 - 18

Between \( t = 14 \) and \( t = 18 \), the y - value (population) increases rapidly (steep slope), so growth is quick. This supports "The population grew relatively quickly between hours 14 and 18."

Step3: Analyze after hour 19

After \( t = 19 \), the y - values are relatively constant (flat line), so population size changes little. This supports "The population size did not change much after hour 19."

Step4: Analyze exponential growth for 24 hours

Exponential growth has a continuously increasing slope. After hour 19, the slope is 0 (flat), so it's not exponential for all 24 hours. So "The population grew exponentially for all 24 hours" is not supported.

Answer:

The population grew relatively slowly for the first 12 hours.
The population grew relatively quickly between hours 14 and 18.
The population size did not change much after hour 19.