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8 February, 22:16

at 10a. m. you consume an energy drink containing 800mg of caffeine. if the half-life of caffeine is 5.7 hours, how much caffeine is in your body at 7p. m.?

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  1. 8 February, 22:33
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    268 mg

    Step-by-step explanation:

    Let A₀ = the original amount of caffeine

    The amount remaining after one half-life is ½A₀.

    After two half-lives, the amount remaining is ½ * ½A₀ = (½) ²A₀.

    After three half-lives, the amount remaining is ½ * (½) ²A₀ = (½) ³A₀.

    We can write a general formula for the amount remaining:

    A = A₀ (½) ⁿ

    where n is the number of half-lives.

    n = t/t_½

    dа ta:

    A₀ = 800 mg

    t₁ = 10 a. m.

    t₂ = 7 p. m.

    t_½ = 5.7 h

    Calculations:

    (a) Calculate t

    t = t₂ - t₁ = 7 p. m. - 10 a. m. = 19:00 - 10:00 = 9:00 = 9.00 h

    (b) Calculate n

    n = 9.00/5.7 = 1.58

    (b) Calculate A

    A = 800 * (½) ^1.58 = 800 * 0.334 = 268 mg

    You will still have 268 mg of caffeine in your body at 10 p. m.
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