Question

curve that levels off as population size approaches the carrying capacity.
bacterial population
complete the sentences.
the bacterial populations growth rate between hours 15 and 16 was
its growth rate between hours 14 and 15.
its growth rate between hours 17 and 18 was
its growth rate
between hours 16 and 17.
its growth rate after 20 hours was

Explanation:

Step1: Analyze growth rate (slope)

Growth rate is the slope of the population - time graph. For a time interval \([t_1,t_2]\), the growth rate is approximately \(\frac{\Delta P}{\Delta t}\), where \(\Delta P = P(t_2)-P(t_1)\) and \(\Delta t=t_2 - t_1\) (here \(\Delta t = 1\) hour for adjacent hours, so growth rate \(\approx\Delta P\)).

Step2: Compare 15 - 16 and 14 - 15

• Between 14 - 15 hours: Let's assume from the graph, the population at \(t = 14\) is low, at \(t = 15\) it's, say, \(P(15)-P(14)=a\).
• Between 15 - 16 hours: The population increase \(\Delta P=P(16)-P(15)\) is larger than \(a\) (since the curve is steepening here). So growth rate 15 - 16 is greater than 14 - 15.

Step3: Compare 17 - 18 and 16 - 17

• Between 16 - 17 hours: The curve is still steep, \(\Delta P_1=P(17)-P(16)\).
• Between 17 - 18 hours: The curve starts to flatten a bit, \(\Delta P_2=P(18)-P(17)\) is less than \(\Delta P_1\). So growth rate 17 - 18 is less than 16 - 17.

Step4: Growth rate after 20 hours

After 20 hours, the curve levels off, so \(\Delta P\approx0\) (since population approaches carrying capacity), so growth rate is approximately 0 (or much lower than before).

Answer:

1. The bacterial population's growth rate between hours 15 and 16 was greater than its growth rate between hours 14 and 15.
2. Its growth rate between hours 17 and 18 was less than its growth rate between hours 16 and 17.
3. Its growth rate after 20 hours was approximately 0 (or very low, approaching 0).