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CalebBeavers

  • 2 years ago

A certain bacteria population is known to triple every 90 minutes. Suppose that there are initially 80 bacteria. What is the size of the population after t hours?

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  1. freewilly922
    • 2 years ago
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    If you know the doubling formula, you can just convert \[P2^{t/k} \to P3^{t/k} \] and use it that way.

  2. freewilly922
    • 2 years ago
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    So if this was doubling instead of tripling you would have \[P(t) = (80)2^{t/90}\] since you want this with respect to hours and not minutes you would convert the 90 minutes to hours or 1.5 so \[P(2) = 80 \times 2^{t/1.5}\] Now just convert this to tripling instead of doubling.

  3. freewilly922
    • 2 years ago
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    And that should be P(t) not P(2). Sorry.

  4. CalebBeavers
    • 2 years ago
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    No idea what that is...its online homework. I think im supposed to use A(t)=(A_0)e^(kt)

  5. CalebBeavers
    • 2 years ago
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    \[A(t)=A _{0}e ^{kt}\]

  6. freewilly922
    • 2 years ago
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    You can use that equation if you want to. It's just harder and more difficult. If, however, there is a population whose growth doubles for a given time span, you can represent the growth by \[A(t) = A_0 2^{t/k}\] where k represents the time it takes to "double". If it was tripling every time span you would use a 3 instead of a 2.

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