A bacterial population B is known to have a rate of growth proportional to B itself. If between12 noon and 2pm the population triplesWhat is the growth rate of the given problem?Is the number of bacterial population important to the problem?At what time should B become 100 times what it was at 12:00 noon assuming that no control are being exerted?

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Andre BalkonE · Accepted Answer

To solve the given problem, let&#039;s break it down step by step.1. Growth rate of the bacterial population:The growth rate of the bacterial population is stated to be proportional to the population itself. We can represent this relationship mathematically as:dBdt=k·BWhere:- dBdt represents the rate of change of the population with respect to time.- k is the proportionality constant.- B represents the population of bacteria at any given time.2. Population tripling between 12 noon and 2 pm:We are given that the population triples between 12 noon and 2 pm. Let&#039;s denote the population at 12 noon as B0 and the population at 2 pm as B2. According to the information provided, we have:B2=3·B03. Growth rate and population importance:The growth rate of the bacteria is important because it determines how fast the population increases. However, in this specific problem, we are not given the value of the growth rate constant (k) or the initial population (B0). We need this information to find the growth rate and solve the problem.4. Finding the time when B becomes 100 times B0:Let&#039;s assume the time at which B becomes 100 times B0 is represented by t hours after 12 noon. We can set up the following equation:B=100·B0Substituting the growth rate equation (from step 1) into this equation, we get:dBdt=k·B100·B0=k·BSince we don&#039;t know the values of B0 or k, we cannot directly solve this equation to find the time t. However, if we had the specific values of B0 and k, we could solve this equation by integrating to find the relationship between B and t.

A bacterial population B is known to have

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