algebra - help please

A thermometer reading 7 degrees C is brought into a room with a constant temperature of 29 degrees C.
If the thermometer reads 15 degrees C after 4 minutes, what will it read in 6 minutes? 11 minutes?

So I guess I need to put into newton's law of cooling:
u(t) = T + (u sub zero - T ) e^kt

How do I solve for k so can plug in my T's. and what is u sub zero? initial what?

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  1. well I put the law like this:

    T(t) = Ts - (Ts-To)e^(-kt)
    Ts = T surroundings = 29
    To = initial Temp = 7

    now put in at 4 min
    T(4) = 15 = 29 - (29-7)e^-4k
    15 = 29 - 22 e^(-4k)
    -14 = 22 e^-4k
    - .636363... = e^-4k
    ln (-.636363 ... ) = -4k
    -4k = -.452
    k = .113
    so you go on and put 6 minutes in for t

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    posted by Damon
  2. Still lost. I put in 6 and lost a variable.
    T(6) = 29 - (29 - 7) e^-0.678
    29 - 22e^-0.678
    -29 = -22e^-0.678
    ln 1.318181818 = e^-0.678
    0.276253377 = -0.678

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