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A population of bacteria increases by 30 every hour. Is this situation linear or exponential?

A) Linear, because the function decreases.
B) Exponential, because the function decreases.
C) Exponential, because the function increases by a common ratio.
D) Linear because the function increases by a difference.

1 Answer

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Final answer:

The population of bacteria that increases by 30 every hour exhibits an exponential growth pattern, characterized by a rate of increase that accelerates over time, resulting in a population size increasing at an ever-greater rate.

Step-by-step explanation:

The situation described where a population of bacteria increases by 30 every hour refers to a condition of exponential growth rather than linear growth. This is characterized by the fact that the number of organisms added in each reproductive generation increases at a greater rate over time. If, for example, 1000 bacteria are placed in a large flask with an unlimited supply of nutrients, after one hour there would be 2000 bacteria, representing an increase of 1000 organisms. After another hour, those 2000 would divide to produce 4000 bacteria, indicating that the number of bacteria doubles every hour. By the third hour, you would expect 8000 bacteria, continuing this accelerating trend. This exponential growth results in a population that is increasing at a greater and greater rate, which can be depicted graphically as a J-shaped growth curve when the population size, N, is plotted over time.

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