Question

as the population’s size gets closer to the environment’s carrying capacity, when the environment has less space and fewer resources available for additional population growth. the size of a population growing logistically over time is modeled by an s - shaped growth curve that levels off as population size approaches the carrying capacity. bacterial population (a chart of bacterial population size over time with time elapsed (hours) on the x - axis from 0 to 24 and population size (in billions) on the y - axis) complete the sentences. the bacterial population’s growth rate between hours 15 and 16 was blank its growth rate between hours 14 and 15. its growth rate between hours 17 and 18 was blank its growth rate between hours 16 and 17. its growth rate after 20 hours was blank.

Explanation:

Step1: Analyze growth rate (slope)

Growth rate is the slope of the population - time graph. Slope between two points \((t_1,P_1)\) and \((t_2,P_2)\) is \(\frac{P_2 - P_1}{t_2 - t_1}\). Since the time interval is 1 hour (\(t_2 - t_1=1\)), growth rate is \(P_2 - P_1\).

Step2: Compare 15 - 16 and 14 - 15

• Between 14 - 15 hours: Let's assume at \(t = 14\), \(P_1\) and at \(t = 15\), \(P_2\). From the graph, the increase in population (slope) between 14 - 15 is less than between 15 - 16. So growth rate between 15 - 16 is greater than between 14 - 15.

Step3: Compare 17 - 18 and 16 - 17

• Between 16 - 17 hours: The slope (increase in population) is steeper than between 17 - 18. So growth rate between 17 - 18 is less than between 16 - 17.

Step4: Growth rate after 20 hours

After 20 hours, the graph levels off, so the slope (growth rate) is approximately 0 (no change in population).

Answer:

1. The bacterial population’s growth rate between hours 15 and 16 was \(\boldsymbol{\text{greater than}}\) its growth rate between hours 14 and 15.
2. Its growth rate between hours 17 and 18 was \(\boldsymbol{\text{less than}}\) its growth rate between hours 16 and 17.
3. Its growth rate after 20 hours was \(\boldsymbol{0}\) (or "approximately 0" or "negligible" as the population levels off).