Answer: a. it doubles
Explanation:
Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.
As the given halide is tertiary halide and the base is strong , it undergoes [tex]SN^1[/tex] reaction and thus rate depends only on the concentration of tert-butyl bromide.
[tex]Rate=k[tertbutylbromide]^1[/tex][base]^0
k= rate constant
If concentration of both the base and the substrate are doubled ,
[tex]Rate'=k[2\times tertbutylbromide]^1[2\times base]^0}[/tex]
[tex]Rate'=k2^1[tertbutylbromide]^1[base]^0[/tex] (2)
[tex]Rate'=2\times Rate[/tex]
Thus the rate of reaction doubles.