This exercise uses the population growth model. The count in a culture of bacter

Question

This exercise uses the population growth model. The count in a culture of bacteria was 400 after 2 hours and 25, 600 after 6 hours. (a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.) (b) What was the initial size of the culture? (Round your answer to the nearest whole number) (e) Find a function that models the number of bacteria n(t) after t hours. (Enter your answer in the form Round your m_0 value to the nearest whole number. Round your r value to two decimal places.) (d) Find the number of bacteria after 4.5 hours (Round your answer to the nearest hundred.) (e) After how many hours will the number of bacteria reach 50,000? ()

Explanation / Answer

The equation of relative growth we need to use is. n(t) = a*e^(r*t)
where, a=initial population number, e= math constant, r= rate of growth, t=time

25600 = A0e^(6r)
400 = A0e^(2r)

Divide the first by the second, and A0 will drop out,

25600/400 = e^(6r)/e^(2r) = e^(4r)

64 = e^(4r)

ln(64) = 4r

r = ln(64)/4 = 1.039720771

Re substitute:
a = 400/e^2(ln64)/4
a=50

Function to use:
n(t) = 50*e^((ln64/4)*t)

Substitute in t = 4.5

Solve when n(t) = 50000 for t

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