Which type of chemical reaction does this equation exemplify? synthesis decomposition double replacement single replacement

The answer is: single replacement.

Single replacement is reaction where neutral element metal or nonmetal become an ion as it replaces another ion in a compound.  

In this balanced chemical reaction magnesium (Mg) replaces copper (Cu).

Magnesium changes oxidation number from 0 to +2 (oxidation) and copper changes oxidation number from +2 to 0 (reduction).

Reactivity series is an empirical progression of a series of metals, arranged by their reactivity from highest to lowest (alkaline metals have highest reactivity and Noble metals lowest reactivity):  

K > Ba > Sr > Na > Ca > Mg > Be > Al > Mn > Zn > Cr> Fe > Cd > Co > Ni > Sn > Pb > H(in acids) > Cu > Hg > Ag.

Metal higher in the reactivity series will displace another and it will be oxidized.