A cup of coffee at 87 degrees Celsius is placed in a room at 23 degrees Celsius. Suppose that the coffee cools at a rate of 1 degrees Celsius per minute when the temperature of the coffee is 70 degrees. The differential equation describing this has the form $\frac{dT}{dt} = k(T-A)$, where
$A =$ , and
$k =$ .
Either from drawing the direction field (try Maple or by hand) or other intuitive means,
the limiting value of $T$ should be