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10 April, 03:08

Jacob consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Jacob's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Jacob's body is 0.2601.

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  1. 10 April, 05:45
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    Answer: 0.87400mg of caffeine.

    Step-by-step explanation:

    You have

    N (t) = N0 (e^-rt) (1)

    as a general Exponential decay equation where N0 is the amount at t=0, N (t) is the amount remaining at time t and r is the exponential decay constant. You're specifically given that after 10 hours, the decay factor is 0.2601, i. e.,

    N (10) / N (0) = N0 (e^-10r) / N0 (e^0) = e^-10r=0.2601 ... (2)

    Taking the last 2 parts of (2) to the power of 0.1t gives

    e^-rt=0.2601^.1t ... (3)

    This means that

    N (t) = N0 (e^-rt) = N0 (0.2601^.1t) ... (4)

    Also,

    N (2.56) N (1.56) = N0 (0.2601.1 (2.56)) N0 (0.2601.1 (1.56)) = 0.2601.1 (2.56-1.56) = 0.2601^.1

    = 0.87400mg of caffeine.
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