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A pot of boiling water at 100C is removed from a stove at time t = o and left to cool in the kitchen. After 5 min, the water temperature has decreased to 80C, and another 5min later it has dropped to 65C. Assume Newtons law of cooling (dT/dt = k(M - T) ) applies, determain the constant temperature (M) of the kitchen.

Okay, so the solution to the differential equation is - T= Ce^(kt) + M and we want to solve for M

T(0) = C +M

100 = C + M

Equation 1.

T(5) = Ce^(k5) + M

80 = Ce^(k5) + M

Equation 2.

T(10) = Ce^(k10) + M

65 = Ce^(k10) + M

Therefore.. the 2 equations are

80 = Ce^(k5) + M

65 = Ce^(k10) + M

and if I subtract them, I get

15 = Ce^(k5) - Ce^(k10)

And this is where im lost. I have no idea how to solve for M

Can somebody help me please?

Thanks

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# Homework Help: Differential Equation Proof

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