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    Hi, i was wondering if anyone could help me on some past C3 questions.

    A radioactive substance is decaying exponentially. Initially its mass is 480g. Its mass, M grams, at a time t years after the initial observation is given by

    M = 480e^(kt)

    where k is a constant. When t = 330, the mass of the substance will be 240g.

    (i) State the value of the mass whenn t = 660.
    (ii) Determine the value of K.
    (iii) Find the rate at which the mass will be decreasing when t = 200.
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    i. Use natural logarithms
    ii. Rearranging algebra
    iii. Rearranging and using t=200
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    (i) Half life remember. Since 330 seconds is the half life of the substance then 480 - 240 - ???. Remember any 'state' questions don't need any working out and are awarded 1 mark most of the time.
    (ii) Put t=330, M=240 and solve
    (iii) Put t=200 and solve. With this value of M, 480-M/200 (I think) to find the rate
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    (Original post by Brianstorm91)
    i. Use natural logarithms
    ii. Rearranging algebra
    iii. Rearranging and using t=200
    dont u have to part ii first inorder to do part i.
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    i) 240 = 480e^(kt)

    1/2 = e^(330k)

    ln .5 = 330k

    k= ln.5 / 330

    ok? then plug in the values 660, and k

    ii) already found ?

    iii) find the derivative, this is the "rate", now plug in 200 into 't'. Done.
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    (Original post by Student#1)
    i) 240 = 480e^(kt)

    1/2 = e^(330k)

    ln .5 = 330k

    k= ln.5 / 330

    ok? then plug in the values 660, and k

    ii) already found ?

    iii) find the derivative, this is the "rate", now plug in 200 into 't'. Done.
    for the last part do you mean dM/dt for the derirative?
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    (Original post by TSR King)
    for the last part do you mean dM/dt for the derirative?
    Yes.
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    (Original post by Student#1)
    Yes.
    I still cant manage part iii, can some one go through it please?
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    (Original post by TSR King)
    I still cant manage part iii, can some one go through it please?
    you need to find dM/dt (think differentiation) and then sub t=200.
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    (Original post by GHOSH-5)
    you need to find dM/dt (think differentiation) and then sub t=200.
    so would dM/dt = t480e^kt

    and then putting t=200.. you get 63070.86851, is that correct?
    ( k = (ln0.5)/330 )
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    (Original post by TSR King)
    so would dM/dt = t480e^kt

    and then putting t=200.. you get 63070.86851, is that correct?
    ( k = (ln0.5)/330 )
    dM/dt is not t480e^kt, but something else. close, but not quite.
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    (Original post by GHOSH-5)
    dM/dt is not t480e^kt, but something else. close, but not quite.
    o yeh its k480e^kt... which gives me: -0.662.. correct?
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    (Original post by TSR King)
    o yeh its k480e^kt... which gives me: -0.662.. correct?
    yeh that's right for dM/dt, and i got the same after plugging it into my calc. :yy:
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    (Original post by GHOSH-5)
    yeh that's right for dM/dt, and i got the same after plugging it into my calc. :yy:
    beautiful.
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    (Original post by TSR King)
    beautiful.
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    (Original post by GHOSH-5)
    Thanks for the help.. Here's another question as i hate functions..

    g: x |-> |x-2|
    f: x |-> 5e^(0.5x) - 6.

    (i) Determine the range of f and g.
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    (Original post by TSR King)
    Thanks for the help.. Here's another question as i hate functions..

    g: x |-> |x-2|
    f: x |-> 5e^(0.5x) - 6.

    (i) Determine the range of f and g.
    g(x): think about what the moduli actually 'do'
    f(x): think about the range of e^x and adapt it to this question. (hint: the 5 and the 0.5 don't really make much difference to the range)
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    (Original post by GHOSH-5)
    g(x): think about what the moduli actually 'do'
    f(x): think about the range of e^x and adapt it to this question. (hint: the 5 and the 0.5 don't really make much difference to the range)
    would the range of g be x>2
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    (Original post by TSR King)
    would the range of g be x>2
    not exactly. counterexample x=2
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    (Original post by GHOSH-5)
    not exactly. counterexample x=2
    x > 0
 
 
 
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