Example

A cup of coffee is poured from a potwhose contents are into a non-insulated cup in a room at . After a minute, the coffee has cooled to . How much time is required before the coffee reaches a drinkable temperature of ?

1. Enter the equation.

     > eq1:= T = exp(k*t+C) +20;
   

   

2. Solve for C by using the initial temperature.

     > eq2:= subs({t=0,T=95},eq1);
   

   

     > C:=evalf(solve(eq2,C));
   

   

3. Solve for k by using the temperature at t=1.

     > eq3:=subs({t=1,T=90},eq1);
   

   

     > k:=solve(eq3,k);
   

   

4. Look at the original equation and notice that the only variable is t. Proceed to enter desired temperature and solve for t.

     > eq1;
   

   

     > eq4:=subs(T=65,eq1);
   

   

     > solve(eq4,t);
   

   

The time it takes for the coffee to reach is 7.4 minutes.