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Homework Help: Ap mult choice

  1. Apr 20, 2004 #1
    Heres an AP multiple choice problem thats giving me some trouble:

    If [tex]\frac{\,dy}{\,dt} = ky [/tex] and k is a nonzero constant, then y could be

    a) [itex] 2e^{kty}[/itex]
    b) [itex] 2e^{kt}[/itex]
    c) [itex] e^{kt} +3[/itex]
    d) [itex] kty + 5 [/itex]
    e) [itex] \frac{1}{2}ky^2 + \frac{1}{2}[/itex]

    Dont quite know where to begin?
  2. jcsd
  3. Apr 20, 2004 #2
    You have two choices.

    #1 (probably the hardest way, but useful if you forgot how to solve it): Take all of the answers and plug them in. See which one works.

    #2: Separate the variables and integrate.

    dy/y = k*dt
    ln(y) = kt + C
    y = e^(kt + c) = Ae^(kt)

  4. Apr 21, 2004 #3


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    Science Advisor

    Actually, for this problem, I suspect that most people would just differentiate each of the answers.
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