If it backfires when you let off the gas peddle it has air getting into the exhaust, either an exhaust gasket or cracked manifold before the catalytic converter or the emission control's Air Injection system. The air injection check valves (STANDARD MOTOR PRODUCTS PT#AV7) are common failure parts. Cost about $18.00 each you should replace both if they are the problem. Be sure to use a wrench on the pipe and a wrench on the valve or the pipe will twist and break and sometimes a torch is required.
If you hear a pop sound under the hood when you accelerate it is most likely running lean (Not enough fuel) from either a vacuum leak or the fuel pump failing (low fuel pressure). The 90 degree elbow in the PCV Valve hose at the base of the throttle body to the PCV valve is common to either fall off or have a hole in it. Most of the time the engine will idle at a higher RPM a suction sound can be heard. The hose is available in the "HELP" section at any Auto Parts store. I think the part is a DORMAN# 46001. If the POP is from the intake you have to check all the vacuum hose connections and the throttle body base gasket because the POP will blow the hoses off and can blow a section out of the base gasket causing an even leaner fuel mixture.