2000 Mitsubishi Eclipse White Smoke from exhaust.

White smoke coming out the tail pipe is indicitave of coolant entering the engine's cylinders. It is usually caused by a failing head gasket or a crack in the cylinder head itselt. If this be the case, you will usually notice a coolant loss from the reservoir or bubbles in the cooling system.
As far as cost of repairs, it depends on the cause. Shop repair costs for the above mentioned causes usually are not cheap. You should have the cooling system pressure tested, determine the cause, and we can go from there. Hope this helps.