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Since f(π) = π^2 < 100, f(10π) = 100π^2 > 100, and f is continuous on the closed interval [π, 10π], the intermediate value theorem ensures the existence of a number c in (π, 10π) such that f(c) = 100.

The temperature f(t) of the body at time t in hours after being introduced to an environment having constant temperature T 0 is f(t)=T 0 +Ce-kt where C and k are constants.. A cup of coffee with temperatures 125 degree F is placed in a freezer with temperature 0 degree F.

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