calculus

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A cold metal bar at -30 degrees Celsius is submerged in a pool maintained at a temperature of 40 degrees Celsius. Half a minute later, the temperature of the bar is 20 degrees Celsius. How long will it take the bar to attain a temperature of 30 degrees Celsius?

I know that dy/dt=k(y-b) and y(t)=b+Ce^kt

  • calculus -

    The solution will be of the form

    T - 40 = (-70)*exp(-kt)

    Note that this satisfies T = -30 when t = 0 and T-> 40 as t -> infinity

    Solve for k by using the fact that
    T = 20 at t = 30 s.
    -20 = -70*exp(-30 t)
    exp(-30k) = 0.2857
    -30k = -1.253
    k = 4.18*10-2
    (1/k) = 23.9 seconds

    Now solve for t when T = 30 C

  • Math -

    I hate this
    Doesn't help for me in any thing

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