Question #3662

I need help on this question. A culture of bacteria grew from 320 to 780 in 5 hours. If this growth continues at this rate then how long will it take the population to triple?

Expert's answer

Let`s assume that bacteria culture grow linearly.

x_{0} = 320, t = 5h, y_{1} = 780

y = αx_{0} t => α = y_{1}/(x_{0} t) = 780/(320*5) = 0.4875

y = 3x_{0} = αx_{0} t => t = (3x_{0})/(αx_{0}) = 3/α = 3/0.4875 = 80/13

So, the population will triple after 80/13 hours.

x

y = αx

y = 3x

So, the population will triple after 80/13 hours.

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