Question

The number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 11% per hour. An initial sample is obtained from this population, and after four hours, the sample has grown to 4130 bacteria. Find the number of bacteria in the initial sample. Round your answer to the nearest integer.

Answer 1

db/dt = 0.11 b
db/b = .11 dt
ln b = .11t + c'
b = e^(.11 t + c') = C e^.11t)
where C is b at t = 0
when t = 4
b = 4130 = C e^.44
ln 4130 = ln C + .44
8.33 =ln C + .44
ln C = 7.89
C = 2670

Answer 2

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