1 pt) A bacteria culture starts with 640 bacteria and grows at a rate proportion

Question

1 pt) A bacteria culture starts with 640 bacteria and grows at a rate proportional to its size. After 5 hours there will be 3200 bacteria.

(a) Express the population after t hours as a function of t.
population: (function of t)

(b) What will be the population after 3 hours?


(c) How long will it take for the population to reach 2970 ?


1 pt) A bacteria culture starts with 640 bacteria and grows at a rate proportional to its size. After 5 hours there will be 3200 bacteria.

(a) Express the population after t hours as a function of t.
population: (function of t)

(b) What will be the population after 3 hours?


(c) How long will it take for the population to reach 2970 ?

Explanation / Answer

1)

dy/dt = k.y

-> y(t) = A.e^(kt)

y(0) = A = 640

y(5) = 640e^(5k) = 3200 -> 5k = ln(3200/640) -> k = 1/5 ln(3200/640) = ln(5)/5 = 0.322

y(t) = 640 e^(0.322t)

b)

y(3) = 640 e^(0.322*3) = 1681

c)

640 e^(0.322*t) = 2970

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