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 ?

- Enter the equation.
> eq1:= T = exp(k*t+C) +20;

- Solve for
*C*by using the initial temperature.> eq2:= subs({t=0,T=95},eq1);

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

- Solve for
*k*by using the temperature at*t*=1.> eq3:=subs({t=1,T=90},eq1);

> k:=solve(eq3,k);

- 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.

Tue Sep 24 13:59:38 EDT 1996