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not to pick nits, but a backfire is out the carb, not the exhaust. What you have is called a MISfire. Which means it's not burning in the combustion chamber but in the exhaust.

And the term misfire refers to and engine 'misfiring' not nessessarly popping through the exhaust although due to the misfire an accumulation of fuel can occur in the exhust system and a explosion that you refer to as as a backfire can occur:
Misfire is a common driveability problem that may or may not be easy to diagnose, depending on the cause. A misfiring cylinder in a four-cylinder engine is, pardon the pun, hard to miss. The loss of 25% of the engine's power
output is the equivalent of a horse trying to run on three legs. The engine may shake so badly at idle that it causes vibrations that can be felt in the steering wheel and throughout the vehicle. The engine also may be hard to start and may even stall at idle, depending on the accessory load (air conditioning, headlights and electric rear defroster, for example).

When misfire occurs, performance suffers along with fuel economy, emissions and idle quality. And, when a misfiring vehicle is subjected to an emissions test, it will usually fail because of the unusually high levels of hydrocarbons (HC) in the exhaust.

What causes a cylinder to misfire? Basically, it's one of three things: loss of spark; the air/fuel mixture is too far out of balance to ignite; or loss of compression. Loss of spark includes anything that prevents coil voltage from jumping the electrode gap at the end of the spark plug. Causes include worn, fouled or damaged spark plugs, bad spark plug wires or even a cracked distributor cap. A weak coil or excessive rotor gas inside a distributor would affect all cylinders, not just a single cylinder.

"Lean misfire" can occur when the air/fuel mixture is too lean (not enough gasoline in the mixture) to burn. This can be caused by a dirty, clogged or inoperative fuel injector; air leaks; or low fuel pressure because of a weak pump, restricted filter or leaky pressure regulator. Low fuel pressure would affect all cylinders rather than an individual cylinder, as would most air leaks. A leaky EGR valve can also have the same effect as an air leak.

Loss of compression means the cylinder loses most of its air/fuel mixture before it can be ignited. The most likely causes here are a leaky (burned) exhaust valve
or a blown head gasket. If two adjacent cylinders are misfiring, it's likely the head gasket between them has failed. Also, if an engine is overheating or losing coolant, it's likely the head gasket is the culprit.

Intermittent misfires are the worst kind to diagnose because the misfire comes and goes depending on engine load or operating conditions. They seem to occur for no apparent reason. The engine may only misfire and run rough when cold but then smooth out as it warms up. Or, it may start and idle fine but then misfire or hesitate when it comes under load. Also, it may run fine most of the time but suddenly misfire or cut out for no apparent reason. Intermittent misfires can be a real challenge to diagnose, so let's start with a steady misfire in one cylinder before moving on to intermittent misfires.

Clean it, if it's Dirty. Oil it, if it Squeaks. But: Don't fix it, if it Works!