Question

for most populations, available resources are limited and restrict how much a population can grow. as a result, most populations cannot exhibit exponential growth forever. consider once again the population of bacteria growing in a petri dish. the petri dish initially contained nutrient agar for food, but no further nutrient agar was added later. the dish also had a lid that kept bacteria from immigrating into or emigrating out of the dish. this graph shows the growth of the population of bacteria over 24 hours. bacterial population graph of bacterial population growth over time select all the statements about this population that are supported by the graph. the population grew by less than 1 billion bacteria over the first 14 hours. the population grew by about 15 billion bacteria between hours 14 and 18. the population grew by less than 1 billion bacteria after hour 19. the population grew exponentially for all 24 hours.

Explanation:

Step1: Analyze first statement

At hour 0, population is ~0. At hour 14, population is ~1 (from graph). Growth: \(1 - 0 < 1\) billion. So first statement is correct.

Step2: Analyze second statement

At hour 14, population ~1. At hour 18, population ~12 (from graph). Growth: \(12 - 1 = 11\), not ~15. So second statement is incorrect.

Step3: Analyze third statement

After hour 19, population is nearly flat. The increase between consecutive points is less than 1 billion. So third statement is correct.

Step4: Analyze fourth statement

Exponential growth has constant percentage growth. The graph flattens (logistic growth), so not exponential for all 24 hours. Fourth statement is incorrect.

Answer:

• The population grew by less than 1 billion bacteria over the first 14 hours.
• The population grew by less than 1 billion bacteria after hour 19.