nstructions: Determine whether the following situation can be modeled by a linear or exponential relationship, and use the model to answer the question.If the number of bacteria in a colony triples every 60 minutes and the population is currently 3,000 bacteria, what will the population be in 240 minutes? Is the growth modeled by a linear function or an exponential function?The population will be Answer 1 Question 12 and it is modeled by a Answer 2 Question 12
Question
nstructions: Determine whether the following situation can be modeled by a linear or exponential relationship, and use the model to answer the question.If the number of bacteria in a colony triples every 60 minutes and the population is currently 3,000 bacteria, what will the population be in 240 minutes? Is the growth modeled by a linear function or an exponential function?The population will be Answer 1 Question 12 and it is modeled by a Answer 2 Question 12
Solution
This situation can be modeled by an exponential relationship, not a linear one. This is because the population of the bacteria is not increasing by a constant amount every 60 minutes, but rather, it is tripling - which is a multiplicative increase.
To calculate the population in 240 minutes, we need to understand that 240 minutes is four 60-minute periods. Since the population triples every 60 minutes, we would multiply the current population by 3, four times.
So, the calculation would be as follows:
3000 bacteria * 3 (after 60 minutes) = 9000 bacteria 9000 bacteria * 3 (after another 60 minutes) = 27000 bacteria 27000 bacteria * 3 (after another 60 minutes) = 81000 bacteria 81000 bacteria * 3 (after another 60 minutes) = 243000 bacteria
So, the population will be 243,000 bacteria in 240 minutes and it is modeled by an exponential function.
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