Answer to Question #74737 in Discrete Mathematics for Guillermo J Aquino

Question

Problem of recursion (Discrete Math)
Assume that changing the temperature of an object during a time interval is proportional to the difference in temperature between the object and the environment. A piece of metal, originally at 1000 degrees farenheight is cooled to 250 degrees farenheight in 5 hours in a medium temperature of 70 degrees farenheight. When will it reach a temperature of 250 degrees farenheight?

{ T(t)=1000 ; t=1
T(t) = { T(t-1)+r[S-T(t-1) ] ; t>1

Where S is the temperature of the medium and r = k.