# Newton's Law of Cooling

1. Homework Statement

A small object of unknown temperature was placed in a large room that had the fixed temperature 30 degrees C. After 10 minutes, the object's temperature is -10 degrees C, and after an additional 10 minutes, the object's temperature was -5 degrees C. What was the initial temperature of the object?

b = 30
When t = 10, y = -10
When t = 20, y = -5

2. Homework Equations

y(t) = b + Ce^(-kt)
dy/dt = -k(y - b)
3. The Attempt at a Solution

When I plug in the knowns of the variables I get either the equation:

-10 = 30 + Ce^(10k)
-or-
-5 = 30 + Ce^(20k)

I'm confused how I can find the constant k value and the constant C value when I'm not given the initial temperature. If someone can help me find either of the constant values I can probably work from there to finish the rest of the problem. Thanks

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When I plug it in I get $$-10 = 30 + Ce^{-10k}, -5 = 30 + Ce^{-20k}$$