SOLUTION: The number of bacteria in a culture doubles every 45 minutes. This situation can be modelled by the function n(t)=nₒ(2)^t/45 where nₒ is the initial number of bacteria and is t

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Question 1181879: The number of bacteria in a culture doubles every 45 minutes. This situation can be modelled by the function n(t)=nₒ(2)^t/45 where nₒ is the initial number of bacteria and is the time in minutes. There is 512 times the initial population at
Answer by math_tutor2020(3817) About Me  (Show Source):
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Notice that 512 is a power of 2, namely 2^9 = 512

This means that after exactly 9 periods, each period being 45 min, the population is 512 times that of the initial count.

So at the 9*45 = 405 minute mark is when the current population is 512 times the initial population.

405 minutes = 360 min + 45 min
405 minutes = (360/60 hr) + 45 min
405 minutes = 6 hr + 45 min


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Answer: 405 minutes (aka 6 hr, 45 min)