A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000. a. Find the initial population b. Find an expression for the population after t hours.
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Rylan Hills
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The bacteria culture has a constant growth rate. Let it be given by N(t) = No*(1 + r)^t
400 = No*(1 + r)^2
50000 = No*(1 + r)^8
(1 + r)^6 = 125
=> 1 + r = 2.2360
No = 400/(1 + r)^2 = 80
The initial number of bacteria is 80 and the expression of their population after t hours is N(t) = 80*(2.2360)^t
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