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...

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.

Asked on by mllysmith

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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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