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18 June, 12:36

A colony of bacteria grows according to the uninhibited growth model. Suppose there is 18 g of bacteria on Monday and 54 g of bacteria on Wednesday.

(a) Find a function that gives the amount of bacteria in grams after t days. (Use the variable a to represent the initial amount.)

A (t) =

(b) What is the doubling time for the colony? (Round your answer to 2 decimal places.)

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  1. 18 June, 12:39
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    a. The general form of equation of an uninhibited growth model is:

    A = a e^kt

    where A is final amount, a is initial amount, k is constant and t is time

    From Monday to Wednesday, two days have passed so t = 2, therefore calculating for constant k:

    54 = 18 e^k (2)

    e^2k = 3

    2k = ln 3

    k = 0.55

    So the function becomes:

    A (t) = a e^0.55t

    b. Finding for t when A = 2a

    2a = a e^0.55 t

    0.55 t = ln 2

    t = 1.26 days
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