Question

A potato is taken from the oven, its temperature having reached 350 degrees. After sitting on a plate in a 70 degree room for 12 minutes, its temperature has dropped to 250 degrees. If Ted will only eat his potato if its between 100 and 150 degrees, will he eat the potato if he arrives home for dinner 20 minutes after the potato came out of the oven? Show all your work and EXPLAIN YOUR REASONING. RATIONALIZE YOUR ANSWER! Assume Newton's Law Of Cooling, which says that the difference between an object's temperature and the ambient temperature is an exponential function of time.

Answer 1

T=70+(350-70)e^-kt
T=70+280e^-kt, when temp is
250=70+280e^-12k
180=280e^-12k
180/280=e^-12k take natural log of both sides
-o.442=-12k
0.03683=k now use this at the equation
T=70+280e^-0.03683t general equation now after t=20min will the temp be between 100 and 150 degrees?
T=70+280e^-0.03683(20min)
T=204 degrees still too hot to eat

Answer 2

lets try 12 min plus 20min, t=32min
T=70+280e^-0.03683(32min)
T=70 degrees ok after 32 min