Growth of bacteria in food products causes a need to "time-date" some products (like milk) so that shoppers will buy the product and consume it before the number of bacteria grows too large and the product goes bad. Suppose that the formula f (t) = 200e0·002t represents the growth of bacteria in a food product. The variable t represents time in days and f (t) represents the number of bacteria in millions. If the product cannot be eaten after the bacteria count reaches 4,000 how long will it take?

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Biology

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27 February, 07:51

Growth of bacteria in food products causes a need to "time-date" some products (like milk) so that shoppers will buy the product and consume it before the number of bacteria grows too large and the product goes bad. Suppose that the formula f (t) = 200e0·002t represents the growth of bacteria in a food product. The variable t represents time in days and f (t) represents the number of bacteria in millions. If the product cannot be eaten after the bacteria count reaches 4,000 how long will it take?

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Conrad Blankenship · Answer 1

Answer: 19,960,039.97 days

Explanation: f (t) = 200e0.002t

where, f (t) is number of bacteria in millions and t is time in days.

so, if the product cannot be eaten after the bacteria count reaches 4000, it will take:

4,000,000,000 = 200e0.002t

4,000,000,000 = 200.4004003t

therefore, t = 4,000,000,000/200.4004003 = 19,960,039.97 days

that is, to say that it will take 19,960,039.97 days before the product will not be eaten again.