Suppose that a rocket is shot up into the air with an initial velocity of 400 ft/sec and loses velocity at the rate of 32 ft/sec each second. After 6 seconds an explosive charge carried by the rocket goes off and adds 100 ft/sec to the speed of the rocket, and thereafter it again loses speed at the rate of 32 ft/sec each second. Write the formula for the speed of the rocket for the interval 0 ≤ t ≤ 15 and graph the function.