A culture of bacteria has an initial population of 77000 bacteria and doubles every 2 hours. Using the formula P_(t)=P_(0)*2^((t)/(d)), where P_(t) is the population after t hours, P_(0) is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 15 hours, to the nearest whole number? Answer:

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A culture of bacteria has an initial population of 77000 bacteria and doubles every 2 hours. Using the formula  P_(t)=P_(0)*2^((t)/(d)), where  P_(t) is the population after  t hours,  P_(0) is the initial population,  t is the time in hours and  d is the doubling time, what is the population of bacteria in the culture after 15 hours, to the nearest whole number? Answer:

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Identify initial population and doubling time: Identify the initial population (P_0) and the doubling time (d). The initial population of bacteria, P_0, is given as 77000 bacteria. The doubling time, d, is given as every 2 hours.Write population formula: Write down the formula for the population after t hours. The formula given is P_(t) = P_(0) * 2^(t/d), where P_(t) is the population after t hours, P_(0) is the initial population, t is the time in hours, and d is the doubling time in hours.Substitute given values: Substitute the given values into the formula. We need to find the population after 15 hours, so t = 15. The initial population P_(0) is 77000, and the doubling time d is 2 hours. Substituting these values into the formula gives us: P_(15) = 77000 * 2^(15/2)Calculate the exponent: Calculate the exponent. To calculate 2^(15/2), we first divide 15 by 2, which gives us 7.5. Then we raise 2 to the power of 7.5. 2^(15/2) = 2^7.5Calculate 2^7.5: Calculate 2^7.5. Using a calculator, we find that 2^7.5 is approximately 181.01933598375618.Multiply by growth factor: Multiply the initial population by the growth factor. Now we multiply the initial population of 77000 by the growth factor we just calculated. P_(15) = 77000 * 181.01933598375618Calculate final population: Calculate the final population. Multiplying 77000 by 181.01933598375618 gives us approximately 13938489.26975618.Round to nearest whole number: Round the population to the nearest whole number. The population of bacteria after 15 hours, rounded to the nearest whole number, is approximately 13938489.

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