Question

The initial size of a culture of bacteria is 2000. after 1 hour the bacteria count is 16000. find a function n(t) = n0ert that models the population.

Answer 1

The initial size of the cultured bacteria was around 2000 after an hour the bacteria count turned to 16000 with the value of n = 8000.

Given:

n = 1000 e^ (kt)

note when t = 0,

e^kt = e^0 = 1

1000*1 ar t = 0

Stepwise solution,

4000/1000 = 4 = e^(k*1)

or

e^k = 4

k = In 4 = 1.386

when n = 1000,

n = 1000 e^(!.386 t)

t = 1.5

n = 1000 e^(2.079)

n = 8000

Hence, the correct answer is (n=4000)

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