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Math Help - continuity...any help?

  1. #1
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    continuity...any help?

    A 0.5 ml dose of a drug is injected into a patient steadily for one second. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.3 % per second. Express Q as a continuous function of t.

    Q(t)= A, 0 < or = to t < or = to 1
    B, 1<t

    A(t)=

    B(t)=
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  2. #2
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    Quote Originally Posted by mer1988 View Post
    A 0.5 ml dose of a drug is injected into a patient steadily for one second. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.3 % per second. Express Q as a continuous function of t.

    Q(t)= A, 0 < or = to t < or = to 1
    B, 1<t

    A(t)=

    B(t)=
    Hello,

    the general form of the equation which describes exponential decay is:

    A(t)=a_0 \cdot e^{k \cdot t}
    A(t) is the amount at the time t
    A_0 is the initial amount
    k isa constant factor which spcify the speed of decaying(?)

    You know that there are left only 0.4985 ml after the first second. This allows us to calculate the constant k:

    0.4985 \ ml = 0.5\ ml \cdot e^{k \cdot 1} will give k \approx -0.00300451

    Therefore the equation of the function is:

    Q(t) = 0.5 \cdot e^{-0.00300451 \cdot t}

    As you may have noticed k \approx -0.3\ \%. You can only use this property for small values of k.
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