A heat-seeking device follows a path such that at time t, its position is a:(t) = (ac(t),y(t)); hence, its velocity is 3'05) = (m'(t),y'(t)). The device is programmed to move in such a way that its velocity always points in the direction in which the temperature is increasing most rapidly. The temperature at the point (as, y) is 11(53):\") = 20 _ $2 _ 4y21 and at t = 0 the device is located at (3, 2). What is the equation of the curve y(:z:) that the device moves along? d E! (Hint: recall that for a parametric carve (:L'(t), y(t)), dy = gt. a: II: dt