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A researchr assistant made 160mg of a radioactive, and found that there was only 20mg left after 45hours.
a) What is the half-life of this substance?
b) Write a function to represent the amount of substance left after x hours
c) If the researcher kew he needed 100mg of the same substance 12 hours after he was able to make a fresh batch, how much should he initially make?

Please help.i have a feeling that something like this will b on my math exam
Please show some steps so I can understand how u get it.

Thanks a bunch I really appreciate it!:)

  • math -

    This is an exponential function of the form
    y=ae^x
    Substituting x,y values (20,45)into the equation,
    20=160*e^(45k)
    take logs on both sides and solve for k
    k=-(1/45)ln(8)
    =-0.04621

    So the mathematical model becomes:
    y(t)=y0*e^(-0.04621t)
    t=time in hours
    y0=initial mass
    y(t)=mass at time t hours.

    Half life (value of t when y(t)/y0=1/2)
    is
    0.5 = e^(-0.04621t)
    Take logs on both sides,
    -0.04621t = ln(0.5)
    t=15

  • math -

    can u do a more simpler way...we never learnt log yet..

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