Question

The count in a bateria culture was 800 after 15 minutes and 1600 after 40 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?

Find the doubling period. ?

Find the population after 65 minutes. ?

When will the population reach 1400?

Answer 1

f1: 800 = B(0) * 2^(15k)
f2: 1600 = B(0) * 2^(40k)

Then f1/f2

f1/f2 = 800/1600 = 2^(-25k)
-> 2^(-1) = 2^(-25k)
-> k = 1/25
doubling period -> 1/k = 25 mins

Initial size
800 = B(0) * 2^(15/25)
-> B(0) = 800 / 2^(15/25) ~ 528

After 65 minutes
f1: 800 = B(0) * 2^(15/25)
f3: B(65) = B(0) * 2^(65/25)
f3/f1 = B(65)/800 = 2^(2) = 4
B(65) = 800 * 4 = 3200

Population 1400, what the time is:
f1: 800 = B(0) * 2^(15/25)
f4: 1400 = B(0) * 2^(t/25)
f4/f1 = 1400/800 = 2^((t-15)25)
1.75 = 2^((t-15)25)
-> log_2(1.75) = (t-15)/25 . log_2(2)
-> (t-15) / 25 = log_2(1.75)
-> (t-15) / 25 ~ 0,807354922
-> t ~ 25 * 0,807354922 + 15
-> t ~ 35,18387305

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Answer 2

yeah i get same answers except i used "e"

Answer 3

when will pop reach 1400? the answer was 118.232075424

Answer 4

but everything else was correct:) thanks

Answer 5

The answer is t ~ 35,18387305 mins

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Answer 6

118???
pop is 1600 when t=40