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Math Help - continuous rate problem

  1. #1
    VkL
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    continuous rate problem

    Please help..

    A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour.

    a.)Write a formula for the amount of , A mg, of caffeine in the body t hours after drinking a cup of coffee.



    How do i handle these type of problems?? what are the variations of this type of problem? Ex.. Half life , double half life..
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  2. #2
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    A = 100(.83)^t where t is in hours.
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  3. #3
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    Quote Originally Posted by VkL View Post
    Please help..

    A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour.

    a.)Write a formula for the amount of , A mg, of caffeine in the body t hours after drinking a cup of coffee.



    How do i handle these type of problems?? what are the variations of this type of problem? Ex.. Half life , double half life..
    If the amount of coffee is x, 17% of that is 0.17x. Where you go from there depends upon what you know. If you know Calculus, you can say that the rate of change is dx/dt so dx/dt= -0.17x. Then dx/x= -0.17dt and, integrating, ln(x)= -0.17t+ c so x= Ce^{-.17t} where C is e^c. If the initial value of x is 100 mg, then x(0)= C= 100 so x(t)= 100e^{-0.17t}
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  4. #4
    VkL
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    thank you very much...is their a basic formual for these type of problems? I remember somethign like A = Ao...then somethign to the rt i think
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