The count in a bateria culture was 600 after 20 minutes and 1600 after 30 minute

Question

The count in a bateria culture was 600 after 20 minutes and 1600 after 30 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?

Find the doubling period:

Find the population after 120 minutes:

When will the population reach 13000.

Explanation / Answer

Dear Student Thank you for using Chegg ! Given that bacteria count grows exponentially P :- Population of bacteria at any time t P0 :- Initial population k :- Rate of increase t :- Time P = P0*e^(kt) Given count in a bateria culture was 600 after 20 minutes and 1600 after 30 minutes. => 600 = P0e^(k*(1/3)) Equation 1 1600 = P0e^(k*(1/2)) Equation 2 Dividing the above 2 equations 0.375 = e^(-k/6) Taking natural log both sides we get -0.98083 = -k/6 k = 5.88498 Substituting in equation 1 and calculating P0 600 = P0e^(5.88498*(1/3)) 600 = 7.111122P0 P0 = 84.37487 Initial Size = 84 b) Doubling period P = P0*e^(kt) P = 2P0 => 2P0 = P0*e^(5.88498*t) 2 = e^(5.88498*t) Taking natural log both sides we get 0.693147 = 5.88498t t = 0.117757 hrs c) Population after 120 mnutes i.e. 2 hrs P = P0*e^(kt) P = 84.37*e^(5.88498*2) P = 10909798 Solution d) When will the population reach 13000 13000 = 84.37e^(5.88498*t) 154.0832 = e^(5.88498*t) Taking natural log both sides 5.037493 = 5.88498*t t = 0.855991 hrs Solution

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