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anonymous

  • 5 years ago

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?

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  1. L
    • 5 years ago
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    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 *

  2. dumbcow
    • 5 years ago
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    yeah i get same answers except i used "e"

  3. anonymous
    • 5 years ago
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    when will pop reach 1400? the answer was 118.232075424

  4. anonymous
    • 5 years ago
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    but everything else was correct:) thanks

  5. L
    • 5 years ago
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    The answer is t ~ 35,18387305 mins *

  6. dumbcow
    • 5 years ago
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    118??? pop is 1600 when t=40

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