If a bacteria population starts with 80 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 80 ·

Question

If a bacteria population starts with 80 bacteria and doubles every four hours, then the number of bacteria after t hours is n = f(t) = 80 · 2t/4. (a) Find the inverse of this function.

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Ella 1 week 2021-09-14T22:10:26+00:00 1 Answer 0

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    2021-09-14T22:11:55+00:00

    Answer:

    Step-by-step explanation:

    given that a bacteria population starts with 80 bacteria and doubles every four hours,

    The function representing the number of bacteria after t hours

    = n=f(t) = 80*2^{\frac{t}{4} }

    We are to find the inverse of the function

    i.e. we must make t = g(n) where g is a function of n.

    Take log on both sides.

    ln n =ln80+\frac{t}{4} ln 2\\\frac{t}{4} =\frac{ln\frac{n}{80} }{ln 2} \\t = 4\frac{ln\frac{n}{80} }{ln 2}

    this is the inverse function.

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